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Journal articles on the topic 'Methods of nonlinear programming'

Author: Grafiati

Published: 28 May 2022

Last updated: 30 July 2025

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1

Nie, Pu-yan. "Sequential penalty quadratic programming filter methods for nonlinear programming." Nonlinear Analysis: Real World Applications 8, no. 1 (2007): 118–29. http://dx.doi.org/10.1016/j.nonrwa.2005.06.003.

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2

Pshenichnyi, B. N., and E. E. Kirik. "Nonlinear programming methods and network flows." Cybernetics and Systems Analysis 30, no. 6 (1994): 846–54. http://dx.doi.org/10.1007/bf02366443.

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3

Patriksson, M. "Partial linearization methods in nonlinear programming." Journal of Optimization Theory and Applications 78, no. 2 (1993): 227–46. http://dx.doi.org/10.1007/bf00939668.

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4

Lin, Ming-Hua, John Gunnar Carlsson, Dongdong Ge, Jianming Shi, and Jung-Fa Tsai. "A Review of Piecewise Linearization Methods." Mathematical Problems in Engineering 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/101376.

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Various optimization problems in engineering and management are formulated as nonlinear programming problems. Because of the nonconvexity nature of this kind of problems, no efficient approach is available to derive the global optimum of the problems. How to locate a global optimal solution of a nonlinear programming problem is an important issue in optimization theory. In the last few decades, piecewise linearization methods have been widely applied to convert a nonlinear programming problem into a linear programming problem or a mixed-integer convex programming problem for obtaining an appro

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5

Chen, Zhong. "Parallel Iterative Methods for Nonlinear Programming Problems." Advanced Materials Research 159 (December 2010): 105–10. http://dx.doi.org/10.4028/www.scientific.net/amr.159.105.

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In this paper, we present two parallel multiplicative algorithms for convex programming. If the objective function is differentiable and convex on the positive orthant of , and it has compact level sets and has a locally Lipschitz continuous gradient, we prove these algorithms converge to a solution of minimization problem. For the proofs there are essentially used the results of sequential methods shown by Eggermont[1].

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6

Ghadimi, Saeed, Guanghui Lan, and Hongchao Zhang. "Generalized Uniformly Optimal Methods for Nonlinear Programming." Journal of Scientific Computing 79, no. 3 (2019): 1854–81. http://dx.doi.org/10.1007/s10915-019-00915-4.

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7

Byrd, Richard H., Jorge Nocedal, and Richard A. Waltz. "Steering exact penalty methods for nonlinear programming." Optimization Methods and Software 23, no. 2 (2008): 197–213. http://dx.doi.org/10.1080/10556780701394169.

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8

Nabatova, D. S. "METHODS OF NONLINEAR PROGRAMMING IN SOLVING FINITE GAMES." SOFT MEASUREMENTS AND COMPUTING 7, no. 80 (2024): 10–20. http://dx.doi.org/10.36871/2618-9976.2024.07.002.

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The paper considers the formulation of nonlinear programming problems for finding a Nash equilibrium situation in a bimatric game and in a game with three participants. An overview of existing methods for solving is given: an algorithm for solving bimatric LemkeHowson games, methods for solving quadratic and convex programming problems for a finite game with three participants.

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9

Aktamovich, Saipnazarov Shaylovbek, Khodjabaeva Dilbar, and Ortiqova Malika. "METHODS FOR SOLVING UN CONDITIONAL AND CONDITIONAL EXTREMUM PROBLEMS." International Journal of Advance Scientific Research 4, no. 6 (2024): 57–65. http://dx.doi.org/10.37547/ijasr-04-06-11.

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The article discusses conditional programming problems. Such problems can in principle, be solved using classical methods. However, along this path there are computational difficulties that make it necessary to search for other solution methods. Therefore, in this article we proposed particular methods for solving nonlinear programming problems.

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10

Białoń, Paweł. "Large-scale nonlinear programming algorithm using projection methods." Discussiones Mathematicae. Differential Inclusions, Control and Optimization 20, no. 2 (2000): 171. http://dx.doi.org/10.7151/dmdico.1011.

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11

Betts,, JT, and I. Kolmanovsky,. "Practical Methods for Optimal Control using Nonlinear Programming." Applied Mechanics Reviews 55, no. 4 (2002): B68. http://dx.doi.org/10.1115/1.1483351.

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12

CHEN, G. J., and A. B. TEMPLEMAN. "ON ENTROPY-BASED METHODS FOR NONLINEAR PROGRAMMING PROBLEMS." Engineering Optimization 23, no. 3 (1995): 225–38. http://dx.doi.org/10.1080/03052159508941355.

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13

Brezhneva, Olga A., and Alexey A. Tret'yakov. "Thep-Factor-Lagrange Methods for Degenerate Nonlinear Programming." Numerical Functional Analysis and Optimization 28, no. 9-10 (2007): 1051–86. http://dx.doi.org/10.1080/01630560701587809.

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14

Forsgren, Anders, and Philip E. Gill. "Primal-Dual Interior Methods for Nonconvex Nonlinear Programming." SIAM Journal on Optimization 8, no. 4 (1998): 1132–52. http://dx.doi.org/10.1137/s1052623496305560.

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15

Lukšan, Ladislav, Ctirad Matonoha, and Jan Vlček. "Interior point methods for large-scale nonlinear programming." Optimization Methods and Software 20, no. 4-5 (2005): 569–82. http://dx.doi.org/10.1080/10556780500140508.

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16

Benson, Hande Y. "Mixed integer nonlinear programming using interior-point methods." Optimization Methods and Software 26, no. 6 (2011): 911–31. http://dx.doi.org/10.1080/10556781003799303.

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17

Ribeiro, Ademir A., Elizabeth W. Karas, and Clóvis C. Gonzaga. "Global Convergence of Filter Methods for Nonlinear Programming." SIAM Journal on Optimization 19, no. 3 (2008): 1231–49. http://dx.doi.org/10.1137/060672285.

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18

Kuriger, Glenn, and Ravi Ravindran. "Intelligent Search Methods For Nonlinear Goal Programming Problems." INFOR: Information Systems and Operational Research 43, no. 2 (2005): 79–92. http://dx.doi.org/10.1080/03155986.2005.11732718.

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19

Kungurtsev, Vyacheslav, and Moritz Diehl. "Sequential quadratic programming methods for parametric nonlinear optimization." Computational Optimization and Applications 59, no. 3 (2014): 475–509. http://dx.doi.org/10.1007/s10589-014-9696-2.

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20

Klopotowski, Jacek. "Linear and nonlinear programming: An introduction to linear methods in mathematical programming." European Journal of Operational Research 25, no. 1 (1986): 145–46. http://dx.doi.org/10.1016/0377-2217(86)90127-x.

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21

Ram, Balasubramanian, and A. J. G. Babu. "Reduction of dimensionality in dynamic programming-based solution methods for nonlinear integer programming." International Journal of Mathematics and Mathematical Sciences 11, no. 4 (1988): 811–14. http://dx.doi.org/10.1155/s0161171288000985.

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This paper suggests a method of formulating any nonlinear integer programming problem, with any number of constraints, as an equivalent single constraint problem, thus reducing the dimensionality of the associated dynamic programming problem.

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22

Onanaye, Adeniyi Samson. "Nonlinear Programming: Theories and Algorithms of Some Unconstrained Optimization Methods (Steepest Descent and Newton's Method)." International Journal of Engineering and Management Research 10, no. 2 (2020): 1–12. https://doi.org/10.31033/ijemr.10.2.1.

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<strong>Nonlinear programming problem (NPP) had become an important branch of operations research, and it was the mathematical programming with the objective function or constraints being nonlinear functions. There were a variety of traditional methods to solve nonlinear programming problems such as bisection method, gradient projection method, the penalty function method, feasible direction method, the multiplier method. But these methods had their specific scope and limitations, the objective function and constraint conditions generally had continuous and differentiable request. The traditio

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23

ADIWIGUNA, I. GEDE WIKAN, G. K. GANDHIADI, and NI MADE ASIH. "PERBANDINGAN METODE SEPARABLE PROGRAMMING DAN QUADRATIC PROGRAMMING DALAM PEMECAHAN MASALAH PEMROGRAMAN NONLINIER." E-Jurnal Matematika 8, no. 4 (2019): 277. http://dx.doi.org/10.24843/mtk.2019.v08.i04.p265.

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The Separable programming method solves nonlinear programming problems by transforming a nonlinear shape that consists of a single variable into a linear function and resolved by the simplex method. Meanwhile, the quadratic programming method accomplishes the two degrees nonlinear model by transforming the nonlinear shape into linear function with the Kuhn Tucker Conditions and resolved by the simplex Wolfe method. Both of these methods are applied to the Markowitz’s portfolio model, which is to find the proportion of stock funds to obtain maximum profits by combination of three shares, such a

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24

Yamashita, Hiroshi, and Hiroshi Yabe. "A SURVEY OF NUMERICAL METHODS FOR NONLINEAR SEMIDEFINITE PROGRAMMING." Journal of the Operations Research Society of Japan 58, no. 1 (2015): 24–60. http://dx.doi.org/10.15807/jorsj.58.24.

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25

Skalecki, Lisa, and Marc Martin. "General adaptive guidance using nonlinear programming constraint-solving methods." Journal of Guidance, Control, and Dynamics 16, no. 3 (1993): 517–22. http://dx.doi.org/10.2514/3.21040.

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26

Li, ChengJin, and WenYu Sun. "On filter-successive linearization methods for nonlinear semidefinite programming." Science in China Series A: Mathematics 52, no. 11 (2009): 2341–61. http://dx.doi.org/10.1007/s11425-009-0168-6.

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27

Ghadimi, Saeed, and Guanghui Lan. "Accelerated gradient methods for nonconvex nonlinear and stochastic programming." Mathematical Programming 156, no. 1-2 (2015): 59–99. http://dx.doi.org/10.1007/s10107-015-0871-8.

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28

Izhutkin, V. S., and M. Yu Kokurin. "Reduced-direction methods with feasible points in nonlinear programming." USSR Computational Mathematics and Mathematical Physics 30, no. 1 (1990): 159–69. http://dx.doi.org/10.1016/0041-5553(90)90025-n.

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29

Wang, Xiao, Shiqian Ma, and Ya-xiang Yuan. "Penalty methods with stochastic approximation for stochastic nonlinear programming." Mathematics of Computation 86, no. 306 (2016): 1793–820. http://dx.doi.org/10.1090/mcom/3178.

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30

Betts, John T., and William P. Huffman. "Large Scale Parameter Estimation Using Sparse Nonlinear Programming Methods." SIAM Journal on Optimization 14, no. 1 (2003): 223–44. http://dx.doi.org/10.1137/s1052623401399216.

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31

Wächter, Andreas, and Lorenz T. Biegler. "Line Search Filter Methods for Nonlinear Programming: Local Convergence." SIAM Journal on Optimization 16, no. 1 (2005): 32–48. http://dx.doi.org/10.1137/s1052623403426544.

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32

Gonçalves, M. L. N., J. G. Melo, and L. F. Prudente. "Augmented Lagrangian methods for nonlinear programming with possible infeasibility." Journal of Global Optimization 63, no. 2 (2015): 297–318. http://dx.doi.org/10.1007/s10898-015-0289-0.

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33

Breitfeld, Marc G., and David F. Shanno. "Computational experience with penalty-barrier methods for nonlinear programming." Annals of Operations Research 62, no. 1 (1996): 439–63. http://dx.doi.org/10.1007/bf02206826.

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34

Benson, Hande Y., and David F. Shanno. "Interior-point methods for nonconvex nonlinear programming: cubic regularization." Computational Optimization and Applications 58, no. 2 (2013): 323–46. http://dx.doi.org/10.1007/s10589-013-9626-8.

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35

Karas, Elizabeth W., Ana P. Oening, and Ademir A. Ribeiro. "Global convergence of slanting filter methods for nonlinear programming." Applied Mathematics and Computation 200, no. 2 (2008): 486–500. http://dx.doi.org/10.1016/j.amc.2007.11.043.

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36

Fukushima, Masao, Keiichi Takazawa, Shuichi Ohsaki, and Toshihide Ibaraki. "Successive linearization methods for large-scale nonlinear programming problems." Japan Journal of Industrial and Applied Mathematics 9, no. 1 (1992): 117–32. http://dx.doi.org/10.1007/bf03167197.

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37

Shanno, David F., and Robert J. Vanderbei. "Interior-point methods for nonconvex nonlinear programming: orderings and higher-order methods." Mathematical Programming 87, no. 2 (2000): 303–16. http://dx.doi.org/10.1007/s101070050116.

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38

Zhou, Zhengyong, and Ting Zhang. "A Comparison of Normal Cone Conditions for Homotopy Methods for Solving Inequality Constrained Nonlinear Programming Problems." Advances in Mathematical Physics 2020 (July 4, 2020): 1–10. http://dx.doi.org/10.1155/2020/5483587.

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Homotopy methods are powerful tools for solving nonlinear programming. Their global convergence can be generally established under conditions of the nonemptiness and boundness of the interior of the feasible set, the Positive Linear Independent Constraint Qualification (PLICQ), which is equivalent to the Mangasarian-Fromovitz Constraint Qualification (MFCQ), and the normal cone condition. This paper provides a comparison of the existing normal cone conditions used in homotopy methods for solving inequality constrained nonlinear programming.

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39

Messerer, Florian, Katrin Baumgärtner, and Moritz Diehl. "Survey of sequential convex programming and generalized Gauss-Newton methods." ESAIM: Proceedings and Surveys 71 (August 2021): 64–88. http://dx.doi.org/10.1051/proc/202171107.

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We provide an overview of a class of iterative convex approximation methods for nonlinear optimization problems with convex-over-nonlinear substructure. These problems are characterized by outer convexities on the one hand, and nonlinear, generally nonconvex, but differentiable functions on the other hand. All methods from this class use only first order derivatives of the nonlinear functions and sequentially solve convex optimization problems. All of them are different generalizations of the classical Gauss-Newton (GN) method. We focus on the smooth constrained case and on three methods to ad

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40

Bachir Cherif, Larbi, and Bachir Merikhi. "A penalty method for nonlinear programming." RAIRO - Operations Research 53, no. 1 (2019): 29–38. http://dx.doi.org/10.1051/ro/2018061.

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This paper presents a variant of logarithmic penalty methods for nonlinear convex programming. If the descent direction is obtained through a classical Newton-type method, the line search is done on a majorant function. Numerical tests show the efficiency of this approach versus classical line searches.

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41

Hidayah, Taufiq, Andry Akhiruyanto, Sri Haryono, and Dewangga Yudhistira. "Linear and nonlinear programming: effects on the physical abilities of young basketball players." Pedagogy of Physical Culture and Sports 28, no. 4 (2024): 274–82. http://dx.doi.org/10.15561/26649837.2024.0404.

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Background and Study Aim. Linear and nonlinear programming are methods used to control intensity and volume in sports training. Despite their widespread application, there is a lack of evidence-based studies that directly compare the effects of linear versus nonlinear programming. This study aims to assess the effect of linear and nonlinear programming on improving the power, agility, and endurance of young basketball players. Material and Methods. This study employs a two-group pretest-posttest experimental design. It included 40 male basketball players aged 16-18, with weights ranging from 6

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42

Jdid, Maissam. "Neutrosophic Nonlinear Models." Prospects for Applied Mathematics and Data Analysis 2, no. 1 (2023): 42–46. http://dx.doi.org/10.54216/pamda.020104.

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Nonlinear programming is an important and essential part of operations research and is more comprehensive than linear programming, its applications have spread in all branches of science, engineering, physics, chemistry, management, economic and military fields, etc. Nonlinear programming can also be used in forecasting, estimation, applied statistics and determining the costs resulting from the production, purchase and storage of goods, the mathematical model is a nonlinear model if any of the vehicles of the target or constraints are nonlinear statements and may be nonlinear statements In bo

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43

Karandey, V. Yu, B. K. Popov, O. B. Popova, and V. L. Afanasyev. "Research of Methods of Optimal Design of Special Electric Drives." Journal of Physics: Conference Series 2096, no. 1 (2021): 012206. http://dx.doi.org/10.1088/1742-6596/2096/1/012206.

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Abstract Problems of optimization of special electrical and electromechanical systems in modeling, creation and design are solved mainly by methods of mathematical programming. The task of mathematical programming is to find extremes of the function of many variables in the presence of restrictions on variables, which creates fundamental difficulties. To solve such problems, the number of methods for solving the general problem of mathematical programming is currently expanding significantly. In this regard, the trend in the development of mathematical programming is following the path of high

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44

Ivanova, L. N., and S. E. Ivanov. "Optimization of Inventory in a Logistics System Using Nonlinear Programming Methods (In Russ.)." Economics Law Innovaion 13, no. 2 (2025): 64–72. https://doi.org/10.17586/2713-1874-2025-2-64-72.

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The article discusses key tasks and methods for optimizing and managing inventory in a logistics system to minimize the total cost of storing goods in a warehouse, as well as optimizing the cost of placing orders based on order volume relative to demand. The aim of the work is to develop a mathematical model for a nonlinear programming problem to minimize costs, taking into account the nonlinear functions of demand and storage costs, as well as inventory and or-der quantity constraints. The authors formulated a nonlinear inventory optimization problem as a nonlinear program-ming problem, for w

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45

V, Gulyayev, and Shlyun N. "OPTIMAL TRACING OF DEEP BOREHOLE TRAJECTORIES BY NONLINEAR PROGRAMMING METHODS." National Transport University Bulletin 1, no. 51 (2022): 127–33. http://dx.doi.org/10.33744/2308-6645-2022-1-51-127-133.

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The issues of rational (optimal) trajectory trajectory of oil and gas wells are apparently one of the few areas of the oil and gas industry that still does not use optimal control and nonlinear programming methods. 133 At the same time, the use of these methods makes it possible to design smoother and shorter trajectories with less risk of emergency situations occurring in them, leading to resonant vibrations of the system, buckling of the drill string and its sticking. In addition, in such columns, the conditions for the hydrodynamic and aerodynamic flow of the working fluid are improved, and

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46

Ito, Satoshi. "Numerical methods of nonlinear optimal control based on mathematical programming." Nonlinear Analysis: Theory, Methods & Applications 30, no. 6 (1997): 3843–54. http://dx.doi.org/10.1016/s0362-546x(96)00327-6.

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47

Kortanek, K. O., Florian Potra, and Yinyu Ye. "On some efficient interior point methods for nonlinear convex programming." Linear Algebra and its Applications 152 (July 1991): 169–89. http://dx.doi.org/10.1016/0024-3795(91)90274-z.

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48

Lundberg, Bruce N., and Aubrey B. Poore. "Numerical Continuation and Singularity Detection Methods for Parametric Nonlinear Programming." SIAM Journal on Optimization 3, no. 1 (1993): 134–54. http://dx.doi.org/10.1137/0803007.

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49

Evtushenko, Yuri G., and Vitali G. Zhadan. "Stable Barrier-projection and Barrier-Newton methods in nonlinear programming." Optimization Methods and Software 3, no. 1-3 (1994): 237–56. http://dx.doi.org/10.1080/10556789408805567.

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50

Schmid, C., and L. T. Biegler. "Acceleration of Reduced Hessian methods for large-scale nonlinear programming." Computers & Chemical Engineering 17, no. 5-6 (1993): 451–63. http://dx.doi.org/10.1016/0098-1354(93)80036-m.

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