Journal articles: 'Fletcher-Reeves method'

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G. Vanaja. "Comparison Between Cauchy's Steepest Descent and Fletcher-Reeves Methods in Solving Unconstrained Neutrosophic Nonlinear Programming Problems." Communications on Applied Nonlinear Analysis 32, no. 2s (2024): 366–85. https://doi.org/10.52783/cana.v32.2411.

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The main objective of this study is to solve unconstrained single-valued Neutrosophic Nonlinear Programming Problems using Cauchy’s Steepest Descent Method(CSDM) and the Fletcher-Reeves Method(FRM). Our approach is based on new arithmetic operations and ranking on the parametric representations of Triangular Neutrosophic Numbers(TNN). We prove some important theorems for Cauchy’s Steepest Descent Method and the Fletcher-Reeves Method. Numerical examples are presented to illustrate the theory developed in this article. The outcomes of the proposed methods are compared.

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Dai, Y. "Convergence properties of the Fletcher-Reeves method." IMA Journal of Numerical Analysis 16, no. 2 (1996): 155–64. http://dx.doi.org/10.1093/imanum/16.2.155.

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Djordjevic, Snezana. "New hybrid conjugate gradient method as a convex combination of FR and PRP methods." Filomat 30, no. 11 (2016): 3083–100. http://dx.doi.org/10.2298/fil1611083d.

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We consider a newhybrid conjugate gradient algorithm,which is obtained fromthe algorithmof Fletcher-Reeves, and the algorithmof Polak-Ribi?re-Polyak. Numerical comparisons show that the present hybrid conjugate gradient algorithm often behaves better than some known algorithms.

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Anam, Syaiful, Mochamad Hakim Akbar Assidiq Maulana, Noor Hidayat, Indah Yanti, Zuraidah Fitriah, and Dwi Mifta Mahanani. "Predicting the Number of COVID-19 Sufferers in Malang City Using the Backpropagation Neural Network with the Fletcher–Reeves Method." Applied Computational Intelligence and Soft Computing 2021 (April 27, 2021): 1–9. http://dx.doi.org/10.1155/2021/6658552.

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COVID-19 is a type of an infectious disease that is caused by the new coronavirus. The spread of COVID-19 needs to be suppressed because COVID-19 can cause death, especially for sufferers with congenital diseases and a weak immune system. COVID-19 spreads through direct contact, wherein the infected individual spreads the COVID-19 virus through cough, sneeze, or close contacts. Predicting the number of COVID-19 sufferers becomes an important task in the effort to curb the spread of COVID-19. Artificial neural network (ANN) is the prediction method that delivers effective results in doing this job. Backpropagation, a type of ANN algorithm, offers predictive problem solving with good performance. However, its performance depends on the optimization method applied during the training process. In general, the optimization method in ANN is the gradient descent method, which is known to have a slow convergence rate. Meanwhile, the Fletcher–Reeves method has a faster convergence rate than the gradient descent method. Based on this hypothesis, this paper proposes a prediction model for the number of COVID-19 sufferers in Malang using the Backpropagation neural network with the Fletcher–Reeves method. The experimental results show that the Backpropagation neural network with the Fletcher–Reeves method has a better performance than the Backpropagation neural network with the gradient descent method. This is shown by the Means Square Error (MSE) resulting from the proposed method which is smaller than the MSE resulting from the Backpropagation neural network with the gradient descent method.

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KIRAN, Kadir. "Geometri Uydurma için En İyi Eşlenik Gradyan Yönteminin Tespit Edilmesi." Konya Journal of Engineering Sciences 10, no. 2 (2022): 366–75. http://dx.doi.org/10.36306/konjes.1003916.

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In this study, it is aimed to determine the optimal conjugate gradient (CG) method for the geometry fitting of 2D measured profiles. To this end, the three well-known CG methods such as the Fletcher-Reeves, Polak-Ribiere and Hestenes-Stiefel were employed. For testing those methods performances, the five primitive geometries accommodating circle, square, triangle, ellipse and rectangle were first built with a 3D printer, and then they were scanned with a coordinate measuring machine (CMM) to achieve their 2D profiles. The nonlinear least squares procedure was implemented to minimize the error between those measured data and modeled ones. An iterative line search was utilized for this task. The search direction was calculated using the above-mentioned CG methods. During the geometry fitting process, the number of function evaluations at each iteration were computed and the total number of function evaluations were set to be a performance measure of the CG method in question when it converged. By using these performance measures, the performance and data profiles were created to efficiently determine the optimal CG method. Based on performance profiles, it can be stated that the Fletcher-Reeves and Polak-Ribiere methods are the fastest ones on three test geometries out of five. In addition to that, all the CG methods were able to complete the geometry fitting of 80% of test geometries. On the other hand, by examining the data profiles, it was determined that the Polak-Ribiere and Hestenes-Stiefel methods achieve their maximum capabilities of the completing geometry fitting (i.e., 80%) with much lower number of function evaluations than the Fletcher-Reeves method. Besides, in most geometries, the Polak-Ribiere method outperformed the others, thereby it was determined to be the optimal one for the geometry fitting. As a conclusion, the reported results in this work might help the end-users who study on the CMM data processing to conduct an efficient geometry fitting.

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Setiawan, Dendy, and Solikhun Solikhun. "Machine Learning Algorithm for Determining the Best Performance in Predicting Turmeric Production in Indonesia." International Journal of Mechanical Computational and Manufacturing Research 11, no. 2 (2022): 50–59. http://dx.doi.org/10.35335/computational.v11i2.1.

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The herb that has many uses in everyday life is turmeric. Not only in Indonesia but in other countries also use turmeric for consumption. Therefore, by making predictions on the level of turmeric production in the country, so that the government or other parties can use this as a reference and reference to solve problems. The method we use is Resilient Backpropagation where this method is one of the methods that is often used to forecast data. By using turmeric plant production data in Indonesia from 2016-2021 taken on the website of the Indonesian Central Statistics Agency. According to the data to be tested a network architecture model is formed, namely 2-15-1, 2-20-1, 2-25- 1 and 2-30-1. From this model, the Fletcher-Reeves method is used. From the 4 models that have been trained and tested, a 2-15-1 model is obtained to be the best architectural model for each method. The accuracy level of the Fletcher-Reeves method with the 2-15-1 model has an MSE value of 0.002481597.

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Jabbar, Hawraz N., Yoksal A. Laylani, Issam A. R. Moghrabi, and Basim A. Hassan. "Development of a New Numerical Conjugate Gradient Technique for Image Processing." WSEAS TRANSACTIONS ON COMPUTER RESEARCH 12 (November 13, 2023): 123–31. http://dx.doi.org/10.37394/232018.2024.12.12.

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We present a new iterative conjugate gradient technique for image processing. The technique is based on a new derivation of the conjugacy coefficient and develops a variant of the classical Fletcher-Reeves conjugate gradient method. The derivation exploits a quadratic function model. The new method is intended to minimize the presence of noise by utilizing the adaptive median filter (AMF) to reduce salt-and-pepper noise, while the adaptive center-weighted median filter (ACWMF) is used to reduce random-valued noise. The theoretical convergence properties of the method are proven and then tested on a basic set of images using MATLAB. The results show that the proposed algorithm is more efficient than the classical Fletcher-Reeves (FR) method, as measured by the signal-to-noise ratio (PSNR). The number of iterations and the number of function evaluations are also lower for the proposed method. The favorable performance of the new algorithm provides promise for deriving similar techniques that enhance the speed and efficiency of image-processing libraries.

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Santos, Rodrigo de S., and Milton J. Porsani. "HYBRID INVERSION OF INTERVAL VELOCITIES IN MULTISCALE APPROACH." Revista Brasileira de Geofísica 35, no. 4 (2017): 237. http://dx.doi.org/10.22564/rbgf.v35i4.1962.

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ABSTRACT. The understanding of the interior of the planet by using the seismic method of reflection requires knowledge of the velocities with which the seismic waves propagate in the subsurface of the Earth. This work presents strategies to obtain the velocity intervals using RMS velocity inversion. Using a hybrid algorithm that combines the Very Fast Simulated Annealing (VFSA) global optimization method and the Fletcher-Reeves local search method, we have sought to reduce the dependence between the accuracy of the results and the model by which the optimization process begins. The main innovative contribution of this study was the development and presentation of the named inversion strategy of multiscale parameters. This technique allows the use of the VFSA method in inversion problems in which the number of variables is significantly large. The hybrid algorithm with multiscale approach was used to solve 1D and 2D problems, estimating models with high degrees of accuracy, which allowed to confirm the efficiency of the proposed method.Keywords: inversion, parameter multiscale, interval velocity, Very Fast Simulated Annealing, Fletcher-Reeves, hybrid.RESUMO. O entendimento do interior do planeta por meio do método sísmico de reflexão requer o conhecimento das velocidades com que as ondas sísmicas se propagam na subsuperfície da Terra. Este trabalho apresenta estratégias para a obtenção das velocidade intervalares por uso inversão de velocidades RMS. Utilizando um algoritmo híbrido, que combina o método de otimização global Very Fast Simulated Annealing (VFSA), e o método de busca local Fletcher-Reeves, buscou-se reduzir a dependência entre a acurácia dos resultados e o modelo pelo qual o processo de otimização se inicia. A principal contribuição inovadora deste estudo foi o desenvolvimento e apresentação da estratégia de inversão nomeada de multiescala de parâmetros. Esta técnica possibilita o uso do método VFSA em problemas de inversão em que o número de variáveis é significativamente grande. O algoritmo híbrido com abordagem multiescala foi usado para solucionar problemas 1D e 2D, estimando modelos com elevado grau de acurácia, o que permitiu confirmar a eficiência do método proposto.Palavras-chave: inversão, multiescala de parâmetros, velocidade intervalar, Very Fast Simulated Annealing, Fletcher-Reeves, híbrido.

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Al-Saidi, Amal. "Improved Fletcher-Reeves Methods Based on New Scaling Techniques." Sultan Qaboos University Journal for Science [SQUJS] 26, no. 2 (2021): 141–51. http://dx.doi.org/10.53539/squjs.vol26iss2pp141-151.

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This paper introduces a scaling parameter to the Fletcher-Reeves (FR) nonlinear conjugate gradient method. The main aim is to improve its theoretical and numerical properties when applied with inexact line searches to unconstrained optimization problems. We show that the sufficient descent and global convergence properties of Al-Baali for the FR method with a fairly accurate line search are maintained. We also consider the possibility of extending this result to less accurate line search for appropriate values of the scaling parameter. The reported numerical results show that several values for the proposed scaling parameter improve the performance of the FR method significantly.

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Dai, Yuhong. "Further insight into the convergence of the Fletcher-Reeves method." Science in China Series A: Mathematics 42, no. 9 (1999): 905–16. http://dx.doi.org/10.1007/bf02880382.

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Kaelo, Pro, Sindhu Narayanan, and M. V. Thuto. "A modified quadratic hybridization of Polak-Ribiere-Polyak and Fletcher-Reeves conjugate gradient method for unconstrained optimization problems." An International Journal of Optimization and Control: Theories & Applications (IJOCTA) 7, no. 2 (2017): 177–85. http://dx.doi.org/10.11121/ijocta.01.2017.00339.

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This article presents a modified quadratic hybridization of the Polak–Ribiere–Polyak and Fletcher–Reeves conjugate gradient method for solving unconstrained optimization problems. Global convergence, with the strong Wolfe line search conditions, of the proposed quadratic hybrid conjugate gradient method is established. We also report some numerical results to show the competitiveness of the new hybrid method.

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Ibrahim, Yahya Ismail, and Hisham Mohammed Khudhur. "Modified three-term conjugate gradient algorithm and its applications in image restoration." Indonesian Journal of Electrical Engineering and Computer Science 28, no. 3 (2022): 1510–17. https://doi.org/10.11591/ijeecs.v28.i3.pp1510-1517.

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In image restoration, the goal is often to bring back a high-quality version of an image from a lower-quality copy of it. In this article, we will investigate one kind of recovery issue, namely recovering photos that have been blurred by noise in digital photographs (sometimes known as "salt and pepper" noise). When subjected to noise at varying frequencies and intensities (30,50,70,90). In this paper, we used the conjugate gradient algorithm to Restorative images and remove noise from them, we developed the conjugate gradient algorithm with three limits using the conjugate condition of Dai and Liao, where the new algorithm achieved the conditions for descent and global convergence under some assumptions. According to the results of the numerical analysis, the recently created approach is unequivocally superior to both the fletcher and reeves (FR) method and the fletcher and reeves three-term (TTFR) metod. Use the structural similarity index measure (SSIM), which is used to measure image quality and the higher its value, the better the result. The original image was compared with all the noisy images and each according to the percentage of noise as well as the images processed with the four methods.

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Abdullah, Zeyad M., Hisham M. Khudhur, and Amera Khairulla Ahmed. "Modification of the new conjugate gradient algorithm to solve nonlinear fuzzy equations." Indonesian Journal of Electrical Engineering and Computer Science 27, no. 3 (2022): 1525. http://dx.doi.org/10.11591/ijeecs.v27.i3.pp1525-1532.

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The conjugate gradient approach is a powerful tool that is used in a variety of areas to solve problems involving large-scale reduction. In this paper, we propose a new parameter in nonlinear conjugate gradient algorithms to solve nonlinear fuzzy equations based on Polak and Ribiere (PRP) method, where we prove the descent and global convergence properties of the proposed algorithm. In terms of numerical results, the new method has been compared with the methods of Fletcher (CD), Fletcher and Reeves (FR), and Polak and Ribiere (PRP). The proposed algorithm has outperformed the rest of the algorithms in the number of iterations and in finding the best value for the function and the best value for the variables.

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Abdullah, Zeyad M., Hisham M. Khudhur, and Amera Khairulla Ahmed. "Modification of the new conjugate gradient algorithm to solve nonlinear fuzzy equations." Indonesian Journal of Electrical Engineering and Computer Science 27, no. 3 (2022): 1525–32. https://doi.org/10.11591/ijeecs.v27.i3.pp1525-1532.

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The conjugate gradient approach is a powerful tool that is used in a variety of areas to solve problems involving large-scale reduction. In this paper, we propose a new parameter in nonlinear conjugate gradient algorithms to solve nonlinear fuzzy equations based on Polak and Ribiere (PRP) method, where we prove the descent and global convergence properties of the proposed algorithm. In terms of numerical results, the new method has been compared with the methods of Fletcher (CD), Fletcher and Reeves (FR), and Polak and Ribiere (PRP). The proposed algorithm has outperformed the rest of the algorithms in the number of iterations and in finding the best value for the function and the best value for the variables.

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Khalil K. Abbo and Hisham M. Khudhur. "New A hybrid conjugate gradient Fletcher-Reeves and Polak-Ribiere algorithm for unconstrained optimization." Tikrit Journal of Pure Science 21, no. 1 (2023): 124–29. http://dx.doi.org/10.25130/tjps.v21i1.962.

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In this Research we developed a New Hybrid method of conjugate gradient type, this Method depends basically on combining Fletcher-Reeves and Polak-Ribiere algorithms by using spectral direction conjugate algorithm, which is developed by Yang Z & Kairong W [19]. The developed method becomes converged by assuming some hypothesis. The numerical results show the efficiency of the developed method for solving test Unconstrained Nonlinear Optimization problems.

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Wang, C. Y., and M. X. Li. "Convergence property of the Fletcher-Reeves conjugate gradient method with errors." Journal of Industrial & Management Optimization 1, no. 2 (2005): 193–200. http://dx.doi.org/10.3934/jimo.2005.1.193.

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Dalla, Carlos Eduardo Rambalducci, Wellington Betencurte da Silva, Júlio Cesar Sampaio Dutra, and Marcelo José Colaço. "A comparative study of gradient-based and meta-heuristic optimization methods using Griewank benchmark function/ Um estudo comparativo de métodos de otimização baseados em gradientes e meta-heurísticos usando a função de benchmark do Griewank." Brazilian Journal of Development 7, no. 6 (2021): 55341–50. http://dx.doi.org/10.34117/bjdv7n6-102.

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Optimization methods are frequently applied to solve real-world problems such, engineering design, computer science, and computational chemistry. This paper aims to compare gradient-based algorithms and the meta-heuristic particle swarm optimization to minimize the multidimensional benchmark Griewank function, a multimodal function with widespread local minima. Several approaches of gradient-based methods such as steepest descent, conjugate gradient with Fletcher-Reeves and Polak-Ribiere formulations, and quasi-Newton Davidon-Fletcher-Powell approach were compared. The results presented showed that the meta-heuristic method is recommended for function with this behavior because is no needed prior information of the search space. The performance comparison includes computation time and convergence of global and local optimum.

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Idress, Amna Weis Mohammed Ahmad, Osman Omer Osman Yousif, Abdulgader Zaid Almaymuni, Awad Abdelrahman Abdalla Mohammed, Mohammed A. Saleh, and Nafisa A. Ali. "A modified type of Fletcher-Reeves conjugate gradient method with its global convergence." Indonesian Journal of Electrical Engineering and Computer Science 33, no. 1 (2024): 425–32. https://doi.org/10.11591/ijeecs.v33.i1.pp425-432.

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The conjugate gradient methods are one of the most important techniques used to address problems involving minimization or maximization, especially nonlinear optimization problems with no constraints at all. That is because of their simplicity and low memory needed. They can be applied in many areas, such as economics, engineering, neural networks, image restoration, machine learning, and deep learning. The convergence of Fletcher-Reeves (FR) conjugate gradient method has been established under both exact and strong Wolfe line searches. However, it is performance in practice is poor. In this paper, to get good numerical performance from the FR method, a little modification is done. The global convergence of the modified version has been established for general nonlinear functions. Preliminary numerical results show that the modified method is very efficient in terms of number of iterations and CPU time.

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ZENG, MEILAN, and GUANGHUI ZHOU. "A MODIFIED FR CONJUGATE GRADIENT METHOD FOR COMPUTING -EIGENPAIRS OF SYMMETRIC TENSORS." Bulletin of the Australian Mathematical Society 94, no. 3 (2016): 411–20. http://dx.doi.org/10.1017/s0004972716000381.

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This paper proposes improvements to the modified Fletcher–Reeves conjugate gradient method (FR-CGM) for computing $Z$-eigenpairs of symmetric tensors. The FR-CGM does not need to compute the exact gradient and Jacobian. The global convergence of this method is established. We also test other conjugate gradient methods such as the modified Polak–Ribière–Polyak conjugate gradient method (PRP-CGM) and shifted power method (SS-HOPM). Numerical experiments of FR-CGM, PRP-CGM and SS-HOPM show the efficiency of the proposed method for finding $Z$-eigenpairs of symmetric tensors.

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Ismail Ibrahim, Yahya, and Hisham Mohammed Khudhur. "Modified three-term conjugate gradient algorithm and its applications in image restoration." Indonesian Journal of Electrical Engineering and Computer Science 28, no. 3 (2022): 1510. http://dx.doi.org/10.11591/ijeecs.v28.i3.pp1510-1517.

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In image restoration, the goal is often to bring back a high-quality version of an image from a lower-quality copy of it. In this article, we will investigate one kind of recovery issue, namely recovering photos that have been blurred by noise in digital photographs (sometimes known as "salt and pepper" noise). When subjected to noise at varying frequencies and intensities (30,50,70,90). In this paper, we used the conjugate gradient algorithm to Restorative images and remove noise from them, we developed the conjugate gradient algorithm with three limits using the conjugate condition of Dai and Liao, where the new algorithm achieved the conditions for descent and global convergence under some assumptions. According to the results of the numerical analysis, the recently created approach is unequivocally superior to both the fletcher and reeves (FR) method and the fletcher and reeves three-term (TTFR) metod. Use the structural similarity index measure (SSIM), which is used to measure image quality and the higher its value, the better the result. The original image was compared with all the noisy images and each according to the percentage of noise as well as the images processed with the four methods.

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Ihsan Daulay, Mochamad Wahyudi, Solikhun, and Lise Pujiastuti. "Determination of the Best Accuracy Model for Predicting Average Years of Schooling using the Fletcher Reeves Algorithm." International Journal of Basic and Applied Science 11, no. 1 (2022): 27–36. http://dx.doi.org/10.35335/ijobas.v11i1.78.

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The average length of schooling is an important and significant factor in looking at the quality of an individual human being, with increasing the quality of human resources it can increase access to decent work which also promises a stable economic income, and to some extent affects the economy in a country. Therefore, a prediction was made. This prediction method uses the Fletcher Reeves algorithm which is an artificial neural network algorithm method for data prediction. However, this paper does not discuss the results of the prediction, but discusses the ability of the Fletcher Reeves neural network algorithm to predict data. The research dataset used in this study is data on the average length of schooling in North Sumatra Province from 2015-2020, this dataset was taken from BPS North Sumatra. The data is then formed into 5 models, namely 2-10-1, 2-15-1, 2-20-1, 2-25-1, 2-30-1. -30-1 with an MSE value of 0.000430727. With these results the 2-30-1 architectural model gets the lowest score, so it can be concluded that the model can be used to predict the average length of schooling in North Sumatra Province.

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Alshorman, Omar, Mustafa Mamat, Ahmad Alhawarat, and Mohd Revaie. "A modifications of conjugate gradient method for unconstrained optimization problems." International Journal of Engineering & Technology 7, no. 2.14 (2018): 21. http://dx.doi.org/10.14419/ijet.v7i2.14.11146.

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The Conjugate Gradient (CG) methods play an important role in solving large-scale unconstrained optimization problems. Several studies have been recently devoted to improving and modifying these methods in relation to efficiency and robustness. In this paper, a new parameter of CG method has been proposed. The new parameter possesses global convergence properties under the Strong Wolfe-Powell (SWP) line search. The numerical results show that the proposed formula is more efficient and robust compared with Polak-Rribiere Ployak (PRP), Fletcher-Reeves (FR) and Wei, Yao, and Liu (WYL) parameters.

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Haikal, Rifani, Mochamad Wahyudi, Lise Pujiastuti, and Solikhun Solikhun. "Fletcher-reeves algorithm for predicting the quantity of production tomato plants in indonesia." International Journal of Mechanical Computational and Manufacturing Research 11, no. 3 (2022): 109–20. http://dx.doi.org/10.35335/computational.v11i3.47.

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The growth of Indonesia's tomato plants continues to increase, and this increase needs to be balanced, according to data from 2015 to 2020. Tomatoes should be used all the time, even in Indonesia. Tomatoes are not only edible but also good for your health and appearance. For the government and various conferences to include this as a point of view in dealing with this problem, it is important to look at the amount of tomato production in Indonesia. Data from the Central Statistics Agency was used to obtain statistics on tomato plant cultivation in Indonesia from 2015 to 2020. This data is solved using the Fletcher-Reeves algorithm using architectural models 2-10-1, 2-20-1, 2-30-1, and 2-35-1. Model 2-10-1 is the best architectural model to predict the amount of tomato production compared to other models, according to the training and testing results of the four models. Model 2-10-1 is used to measure the accuracy of the Fletcher-Reeves method, with MSE Training set at 0.00008463 and MSE Testing at 0.0006094.

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Rana, Z. Al-Kawaz, Y. Al-Bayati Abbas, and S. Jameel Marwan. "Interaction between un updated FR-CG algorithms with optimal Cuckoo algorithm." Indonesian Journal of Electrical Engineering and Computer Science 19, no. 3 (2021): 1497–504. https://doi.org/10.11591/ijeecs.v19.i3.pp1497-1504.

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In this article, we have derived two versions and were derived from an algorithm based on the first suggested modified Fletcher-Reeves method in the article for the two-term CG method and another term to get a downward search towards the function minimum point with the search for an inaccurate line and we have proved rapprochement. These two algorithms combined with the Cuckoo algorithm to achieve a remarkable performance in reducing the number of repetitions in order to reach the minimization of 10 functions is unconstrained in the numerical results.

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Alsuliman, Saleh Nazzal, Mustafa Mamat, Mohd Rivaie, and Ibrahim Sulaiman. "A Combination of FR and HS Coefficient in Conjugate Gradient Method for Unconstrained Optimization." Malaysian Journal of Computing and Applied Mathematics 2, no. 1 (2019): 42–50. http://dx.doi.org/10.37231/myjcam.2019.2.1.28.

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The conjugate gradient (CG) method is one of the most popular methods for solving large-scale problems of unconstrained optimization. In this paper, a new CG method based on combination of two classical CG methods of Fletcher-Reeves (FR), and Hestence-Stiefel (HS) is proposed. This method possess the global convergence properties and the sufficient descent condition. The tests of the new CG method by using MATLAB are measured in terms of central processing unit (CPU) time and iteration numbers with strong Wolfe-Powell inexact line search. Results presented have shown that the new CG method performs better compare to other CG methods.

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Li, Dong-Hui, and Xiao-Lin Wang. "A modified Fletcher-Reeves-Type derivative-free method for symmetric nonlinear equations." Numerical Algebra, Control & Optimization 1, no. 1 (2011): 71–82. http://dx.doi.org/10.3934/naco.2011.1.71.

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Pang, Deyan, Shouqiang Du, and Jingjie Ju. "The smoothing Fletcher-Reeves conjugate gradient method for solving finite minimax problems." ScienceAsia 42, no. 1 (2016): 40. http://dx.doi.org/10.2306/scienceasia1513-1874.2016.42.040.

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Abubakar, Auwal Bala, Kanikar Muangchoo, Abdulkarim Hassan Ibrahim, Jamilu Abubakar, and Sadiya Ali Rano. "FR-type algorithm for finding approximate solutions to nonlinear monotone operator equations." Arabian Journal of Mathematics 10, no. 2 (2021): 261–70. http://dx.doi.org/10.1007/s40065-021-00313-5.

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AbstractThis paper focuses on the problem of convex constraint nonlinear equations involving monotone operators in Euclidean space. A Fletcher and Reeves type derivative-free conjugate gradient method is proposed. The proposed method is designed to ensure the descent property of the search direction at each iteration. Furthermore, the convergence of the proposed method is proved under the assumption that the underlying operator is monotone and Lipschitz continuous. The numerical results show that the method is efficient for the given test problems.

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Devia Narvaez, Diana Marcela, Fernando Mesa, and German Correa Vélez. "Comparison descent directions for Conjugate Gradient Method." Scientia et Technica 26, no. 04 (2021): 518–24. http://dx.doi.org/10.22517/23447214.24893.

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In the following manuscript we will show as a starting point a theoretical analysis of the gradient method, known as one of the first descent methods, and from this we will identify the strength of the conjugate gradient methods. Taking an objective function, we will determine the values that optimize it by means of different methods, indicating the differences of geometric type that these have. Different systems will be used, in order to serve as a test, obtaining their solution in each case and finding the speed at which they converge in accordance with the conjugate gradient methods proposed by Hestenes-Stiefel and Fletcher-Reeves.

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Basim, A. Hassan, N. Jabbar Hawraz, Abdul Rahman Moghrabi Issam, and Joma Alissa Ali. "An enhanced fletcher-reeves-like conjugate gradient methods for image restoration." International Journal of Electrical and Computer Engineering (IJECE) 13, no. 6 (2023): 6268–76. https://doi.org/10.11591/ijece.v13i6.pp6268-6276.

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Noise is an unavoidable aspect of modern camera technology, causing a decline in the overall visual quality of the images. Efforts are underway to diminish noise without compromising essential image features like edges, corners, and other intricate structures. Numerous techniques have already been suggested by many researchers for noise reduction, each with its unique set of benefits and drawbacks. Denoising images is a basic challenge in image processing. We describe a two-phase approach for removing impulse noise in this study. The adaptive median filter (AMF) for salt-and-pepper noise identifies noise candidates in the first phase. The second step minimizes an edge-preserving regularization function using a novel hybrid conjugate gradient approach. To generate the new improved search direction, the new algorithm takes advantage of two well-known successful conjugate gradient techniques. The descent property and global convergence are proven for the new methods. The obtained numerical results reveal that, when applied to image restoration, the new algorithms are superior to the classical fletcher reeves (FR) method in the same domain in terms of maintaining image quality and efficiency

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Hepzibah, R. Irene, and S. Shilpa Ivin Emimal. "On Solving Neutrosophic Unconstrained Optimization Problems by Steepest Descent Method and Fletcher Reeves Method." International Journal of Fuzzy Mathematical Archive 19, no. 02 (2021): 111–22. http://dx.doi.org/10.22457/ijfma.v19n2a02230.

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In this paper, we proposed a method for solving unconstrained optimization problems by Newton’s method with single-valued neutrosophic triangular fuzzy number coefficients. Also, some numerical examples demonstrate the effectiveness of the proposed algorithm. MATLAB programs are also developed for the proposed method.

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32

Hassan, Basim A., Hawraz N. Jabbar, Yoksal A. Laylani, Issam Abdul Rahman Moghrabi, and Ali Joma Alissa. "An enhanced fletcher-reeves-like conjugate gradient methods for image restoration." International Journal of Electrical and Computer Engineering (IJECE) 13, no. 6 (2023): 6268. http://dx.doi.org/10.11591/ijece.v13i6.pp6268-6276.

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Noise is an unavoidable aspect of modern camera technology, causing a decline in the overall visual quality of the images. Efforts are underway to diminish noise without compromising essential image features like edges, corners, and other intricate structures. Numerous techniques have already been suggested by many researchers for noise reduction, each with its unique set of benefits and drawbacks. Denoising images is a basic challenge in image processing. We describe a two-phase approach for removing impulse noise in this study. The adaptive median filter (AMF) for salt-and-pepper noise identifies noise candidates in the first phase. The second step minimizes an edge-preserving regularization function using a novel hybrid conjugate gradient approach. To generate the new improved search direction, the new algorithm takes advantage of two well-known successful conjugate gradient techniques. The descent property and global convergence are proven for the new methods. The obtained numerical results reveal that, when applied to image restoration, the new algorithms are superior to the classical fletcher reeves (FR) method in the same domain in terms of maintaining image quality and efficiency.

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Adeleke, Olawale J., Idowu A. Osinuga, and Raufu A. Raji. "A Globally Convergent Hybrid FR-PRP Conjugate Gradient Method for Unconstrained Optimization Problems." WSEAS TRANSACTIONS ON MATHEMATICS 20 (January 7, 2022): 736–44. http://dx.doi.org/10.37394/23206.2021.20.78.

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In this paper, a new conjugate gradient (CG) parameter is proposed through the convex combination of the Fletcher-Reeves (FR) and Polak-Ribiére-Polyak (PRP) CG update parameters such that the conjugacy condition of Dai-Liao is satisfied. The computational efficiency of the PRP method and the convergence profile of the FR method motivated the choice of these two CG methods. The corresponding CG algorithm satisfies the sufficient descent property and was shown to be globally convergent under the strong Wolfe line search procedure. Numerical tests on selected benchmark test functions show that the algorithm is efficient and very competitive in comparison with some existing classical methods.

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34

Weis Mohammed Ahmad Idress, Amna, Osman Omer Osman Yousif, Abdulgader Zaid Almaymuni, Awad Abdelrahman Abdalla Mohammed, Mohammed A. Saleh, and Nafisa A. Ali. "A modified type of Fletcher-Reeves conjugate gradient method with its global convergence." Indonesian Journal of Electrical Engineering and Computer Science 33, no. 1 (2024): 425. http://dx.doi.org/10.11591/ijeecs.v33.i1.pp425-432.

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The conjugate gradient methods are one of the most important techniques used to address problems involving minimization or maximization, especially nonlinear optimization problems with no constraints at all. That is because of their simplicity and low memory needed. They can be applied in many areas, such as economics, engineering, neural networks, image restoration, machine learning, and deep learning. The convergence of Fletcher-Reeves (FR) conjugate gradient method has been established under both exact and strong Wolfe line searches. However, it is performance in practice is poor. In this paper, to get good numerical performance from the FR method, a little modification is done. The global convergence of the modified version has been established for general nonlinear functions. Preliminary numerical results show that the modified method is very efficient in terms of number of iterations and CPU time.

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35

Chen, Chen, Yi Ma, and Guangbo Ren. "A Convolutional Neural Network with Fletcher–Reeves Algorithm for Hyperspectral Image Classification." Remote Sensing 11, no. 11 (2019): 1325. http://dx.doi.org/10.3390/rs11111325.

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Deep learning models, especially the convolutional neural networks (CNNs), are very active in hyperspectral remote sensing image classification. In order to better apply the CNN model to hyperspectral classification, we propose a CNN model based on Fletcher–Reeves algorithm (F–R CNN), which uses the Fletcher–Reeves (F–R) algorithm for gradient updating to optimize the convergence performance of the model in classification. In view of the fact that there are fewer optional training samples in practical applications, we further propose a method of increasing the number of samples by adding a certain degree of perturbed samples, which can also test the anti-interference ability of classification methods. Furthermore, we analyze the anti-interference and convergence performance of the proposed model in terms of different training sample data sets, different batch training sample numbers and iteration time. In this paper, we describe the experimental process in detail and comprehensively evaluate the proposed model based on the classification of CHRIS hyperspectral imagery covering coastal wetlands, and further evaluate it on a commonly used hyperspectral image benchmark dataset. The experimental results show that the accuracy of the two models after increasing training samples and adjusting the number of batch training samples is improved. When the number of batch training samples is continuously increased to 350, the classification accuracy of the proposed method can still be maintained above 80.7%, which is 2.9% higher than the traditional one. And its time consumption is less than that of the traditional one while ensuring classification accuracy. It can be concluded that the proposed method has anti-interference ability and outperforms the traditional CNN in terms of batch computing adaptability and convergence speed.

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36

Yao, Teng-Teng, Zheng-Jian Bai, Zhi Zhao, and Wai-Ki Ching. "A Riemannian Fletcher--Reeves Conjugate Gradient Method for Doubly Stochastic Inverse Eigenvalue Problems." SIAM Journal on Matrix Analysis and Applications 37, no. 1 (2016): 215–34. http://dx.doi.org/10.1137/15m1023051.

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37

Li, Can, and Dong-Hui Li. "An extension of the Fletcher–Reeves method to linear equality constrained optimization problem." Applied Mathematics and Computation 219, no. 23 (2013): 10909–14. http://dx.doi.org/10.1016/j.amc.2013.04.055.

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38

Zavgorodnii, V. V., A. A. Zavgorodnya, and H. G. Sidenkov. "DEVELOPMENT OF SOFTWARE FOR VISUALIZATION OF ROCKS BASED ON THE FLETCHER-REEVES METHOD." Scientific notes of Taurida National V.I. Vernadsky University. Series: Technical Sciences, no. 5 (2023): 128–32. http://dx.doi.org/10.32782/2663-5941/2023.5/21.

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39

Abubakar, Auwal Bala, Poom Kumam, Hassan Mohammad, Aliyu Muhammed Awwal, and Kanokwan Sitthithakerngkiet. "A Modified Fletcher–Reeves Conjugate Gradient Method for Monotone Nonlinear Equations with Some Applications." Mathematics 7, no. 8 (2019): 745. http://dx.doi.org/10.3390/math7080745.

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One of the fastest growing and efficient methods for solving the unconstrained minimization problem is the conjugate gradient method (CG). Recently, considerable efforts have been made to extend the CG method for solving monotone nonlinear equations. In this research article, we present a modification of the Fletcher–Reeves (FR) conjugate gradient projection method for constrained monotone nonlinear equations. The method possesses sufficient descent property and its global convergence was proved using some appropriate assumptions. Two sets of numerical experiments were carried out to show the good performance of the proposed method compared with some existing ones. The first experiment was for solving monotone constrained nonlinear equations using some benchmark test problem while the second experiment was applying the method in signal and image recovery problems arising from compressive sensing.

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40

Zedan, Adnan Jayed, Eman M. Farhan Al-Douri, and Wessam A. Aules. "Economical Design of Circular Footings Adjacent to Slopes on Sandy Soils." Tikrit Journal of Engineering Sciences 15, no. 3 (2008): 48–62. http://dx.doi.org/10.25130/tjes.15.3.04.

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The analysis presented here introduces three optimization techniques namely, Hooke and Jeeves, Fletcher-Reeves and Davidon-Fletcher-Powell as applied to design of the circular footing adjacent to slopes. A computer program was developed to solve this design problem using the conventional structural design approach in conjunction with these methods, A simple study was performed to detect the sensitivity of the objective function to its design variables. A further parametric study was performed regarding the geometric configurations of the footing and loading conditions in order to provide the geotechnical engineer with some useful design curves. Hooke and Jeeves method has been proved to be very instructive in exposing the effect of the other methods. It has been proved that the minimum cost of the circular footing increases with the increase of the load whereas it decreases as the angle of internal friction increases and the Dcl/B ratio (column diameter/diameter of footing).

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41

Hasibuan, Eka Hayana, Surya Hendraputra, GS Achmad Daengs, and Liharman Saragih. "Comparison Fletcher-Reeves and Polak-Ribiere ANN Algorithm for Forecasting Analysis." Journal of Physics: Conference Series 2394, no. 1 (2022): 012008. http://dx.doi.org/10.1088/1742-6596/2394/1/012008.

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Abstract Each method and algorithm ANN has different performances depending on the algorithm used and the parameters given. The purpose of this research is to obtain the best algorithm information from the two algorithms that will be compared based on the performance value or the smallest / lowest MSE value so that it can be used as a reference and information for solving forecasting problems. The ANN algorithms compared were Conjugate Gradient Fletcher-Reeves and Conjugate Gradient Polak-Ribiere. The conjugate gradient algorithm can solve unlimited optimization problems and is much more efficient than gradient descent-based algorithms because of its faster turnaround time and less iteration. The research data used for the forecasting analysis of the two algorithms are data on the number of rural poor people in Sumatra, Indonesia. 6-10-1, 6-15-1, and 6-20-1 architectural analysis. The results showed that the Polak-Ribiere Conjugate Gradient algorithm with the 6-10-1 architecture has the best performance results and the smallest / lowest MSE value compared to the Fletcher-Reeves algorithm and two other architectures. So it can be concluded that the 6-10-1 architectural architecture with the Conjugate Gradient Polak-Ribiere algorithm can be used to solve forecasting problems because the training time to achieve convergence is not too long, and the resulting performance is quite good.

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42

Sellami, Badreddine, and Mohamed Chiheb Eddine Sellami. "Global convergence of a modified Fletcher–Reeves conjugate gradient method with Wolfe line search." Asian-European Journal of Mathematics 13, no. 04 (2019): 2050081. http://dx.doi.org/10.1142/s1793557120500813.

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In this paper, we are concerned with the conjugate gradient methods for solving unconstrained optimization problems. we propose a modified Fletcher–Reeves (abbreviated FR) [Function minimization by conjugate gradients, Comput. J. 7 (1964) 149–154] conjugate gradient algorithm satisfying a parametrized sufficient descent condition with a parameter [Formula: see text] is proposed. The parameter [Formula: see text] is computed by means of the conjugacy condition, thus an algorithm which is a positive multiplicative modification of the Hestenes and Stiefel (abbreviated HS) [Methods of conjugate gradients for solving linear systems, J. Res. Nat. Bur. Standards Sec. B 48 (1952) 409–436] algorithm is obtained, which produces a descent search direction at every iteration that the line search satisfies the Wolfe conditions. Under appropriate conditions, we show that the modified FR method with the strong Wolfe line search is globally convergent of uniformly convex functions. We also present extensive preliminary numerical experiments to show the efficiency of the proposed method.

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43

Sun, Min, Jing Liu, and Yaru Wang. "Two Improved Conjugate Gradient Methods with Application in Compressive Sensing and Motion Control." Mathematical Problems in Engineering 2020 (May 5, 2020): 1–11. http://dx.doi.org/10.1155/2020/9175496.

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To solve the monotone equations with convex constraints, a novel multiparameterized conjugate gradient method (MPCGM) is designed and analyzed. This kind of conjugate gradient method is derivative-free and can be viewed as a modified version of the famous Fletcher–Reeves (FR) conjugate gradient method. Under approximate conditions, we show that the proposed method has global convergence property. Furthermore, we generalize the MPCGM to solve unconstrained optimization problem and offer another novel conjugate gradient method (NCGM), which satisfies the sufficient descent property without any line search. Global convergence of the NCGM is also proved. Finally, we report some numerical results to show the efficiency of two novel methods. Specifically, their practical applications in compressive sensing and motion control of robot manipulator are also investigated.

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44

AL-BAALI, M. "Descent Property and Global Convergence of the Fletcher—Reeves Method with Inexact Line Search." IMA Journal of Numerical Analysis 5, no. 1 (1985): 121–24. http://dx.doi.org/10.1093/imanum/5.1.121.

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45

Jabbar, Hawraz N., and Basim A. Hassan. "Two-versions of descent conjugate gradient methods for large-scale unconstrained optimization." Indonesian Journal of Electrical Engineering and Computer Science 22, no. 3 (2021): 1643–49. https://doi.org/10.11591/ijeecs.v22.i3.pp1643-1649.

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The conjugate gradient methods are noted to be exceedingly valuable for solving large-scale unconstrained optimization problems since it needn't the storage of matrices. Mostly the parameter conjugate is the focus for conjugate gradient methods. The current paper proposes new methods of parameter of conjugate gradient type to solve problems of large-scale unconstrained optimization. A Hessian approximation in a diagonal matrix form on the basis of second and third-order Taylor series expansion was employed in this study. The sufficient descent property for the proposed algorithm are proved. The new method was converged globally. This new algorithm is found to be competitive to the algorithm of fletcher-reeves (FR) in a number of numerical experiments.

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46

Alkawaz, Rana Z., Abbas Y. AlBayati, and Marwan S. Jameel. "Interaction between updated FR-CG algorithms with optimal Cuckoo algorithm." Indonesian Journal of Electrical Engineering and Computer Science 19, no. 3 (2020): 1497. http://dx.doi.org/10.11591/ijeecs.v19.i3.pp1497-1504.

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In this article we have derived two versions, ξk and ρk were derived from an algorithm based on the first suggested modified Fletcher-Reeves method in the article for the two-term CG method and another term to get a downward search towards the function minimum point with the search for an inaccurate line and we have proved rapprochement. These two algorithms combined with the Cuckoo algorithm to achieve a remarkable performance in reducing the number of repetitions in order to reach the minimization of 10 functions is unconstrained in the numerical results.

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47

Sinaga, Rapianto, Mora Malemta Sitomorang, Deri Setiawan, Anjar Wanto, and Agus Perdana Windarto. "Akurasi Algoritma Fletcher-Reeves untuk Prediksi Ekspor Karet Remah Berdasarkan Negara Tujuan Utama." Journal of Informatics Management and Information Technology 2, no. 3 (2022): 91–99. http://dx.doi.org/10.47065/jimat.v2i3.170.

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Crumb rubber is a natural rubber specially designed to ensure its technical quality. Rubber is produced mainly in Southeast Asia, where Indonesia is the second largest producer in the world after Thailand. This study aims to predict the export of powdered rubber in Indonesia. The prediction method used is FletcherReeves which is one of the artificial neural network methods commonly used to predict data. The research data used is crumb rubber export data by main destination country for the period 2012-2020 which was obtained from the website of the Indonesian Central Statistics Agency. Based on this data, network architecture models will be trained and defined, including 7-10-1, 7-15-1, 7-20-1, 7-25-1, 7-30-1 (trancgf). Of the five models, after training and testing, the best data architecture model is 7-15-1 (trancegf) 7 is the input layer, 15 is the number of neurons in the hidden layer and 1 is the exit layer. The level of accuracy of the architectural model with the MSE value is 0.00482054.

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48

Kannan, B. K., and S. N. Kramer. "An Augmented Lagrange Multiplier Based Method for Mixed Integer Discrete Continuous Optimization and Its Applications to Mechanical Design." Journal of Mechanical Design 116, no. 2 (1994): 405–11. http://dx.doi.org/10.1115/1.2919393.

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An algorithm for solving nonlinear optimization problems involving discrete, integer, zero-one, and continuous variables is presented. The augmented Lagrange multiplier method combined with Powell’s method and Fletcher and Reeves Conjugate Gradient method are used to solve the optimization problem where penalties are imposed on the constraints for integer/discrete violations. The use of zero-one variables as a tool for conceptual design optimization is also described with an example. Several case studies have been presented to illustrate the practical use of this algorithm. The results obtained are compared with those obtained by the Branch and Bound algorithm. Also, a comparison is made between the use of Powell’s method (zeroth order) and the Conjugate Gradient method (first order) in the solution of these mixed variable optimization problems.

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49

Jabbar, Hawraz N., and Basim A. Hassan. "Two-versions of descent conjugate gradient methods for large-scale unconstrained optimization." Indonesian Journal of Electrical Engineering and Computer Science 22, no. 3 (2021): 1643. http://dx.doi.org/10.11591/ijeecs.v22.i3.pp1643-1649.

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The conjugate gradient methods are noted to be exceedingly valuable for solving large-scale unconstrained optimization problems since it needn't the storage of matrices. Mostly the parameter conjugate is the focus for conjugate gradient methods. The current paper proposes new methods of parameter of conjugate gradient type to solve problems of large-scale unconstrained optimization. A Hessian approximation in a diagonal matrix form on the basis of second and third-order Taylor series expansion was employed in this study. The sufficient descent property for the proposed algorithm are proved. The new method was converged globally. This new algorithm is found to be competitive to the algorithm of fletcher-reeves (FR) in a number of numerical experiments.

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50

Zhang, Li, Weijun Zhou, and Donghui Li. "Global convergence of a modified Fletcher–Reeves conjugate gradient method with Armijo-type line search." Numerische Mathematik 104, no. 4 (2006): 561–72. http://dx.doi.org/10.1007/s00211-006-0028-z.

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Journal articles on the topic 'Fletcher-Reeves method'

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