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Journal articles on the topic 'KKT Conditions'

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Published: 4 June 2021

Last updated: 4 February 2022

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1

Facchinei, Francisco, Christian Kanzow, and Simone Sagratella. "Solving quasi-variational inequalities via their KKT conditions." Mathematical Programming 144, no. 1-2 (February 12, 2013): 369–412. http://dx.doi.org/10.1007/s10107-013-0637-0.

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2

Nobakhtian, S., and M. R. Pouryayevali. "KKT Optimality Conditions and Nonsmooth Continuous Time Optimization Problems." Numerical Functional Analysis and Optimization 32, no. 11 (November 2011): 1175–89. http://dx.doi.org/10.1080/01630563.2011.592961.

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3

Ye, Jane J. "Constraint Qualifications and KKT Conditions for Bilevel Programming Problems." Mathematics of Operations Research 31, no. 4 (November 2006): 811–24. http://dx.doi.org/10.1287/moor.1060.0219.

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4

Rahman, Md Sadikur, Ali Akbar Shaikh, Irfan Ali, Asoke Kumar Bhunia, and Armin Fügenschuh. "A Theoretical Framework for Optimality Conditions of Nonlinear Type-2 Interval-Valued Unconstrained and Constrained Optimization Problems Using Type-2 Interval Order Relations." Mathematics 9, no. 8 (April 19, 2021): 908. http://dx.doi.org/10.3390/math9080908.

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In the traditional nonlinear optimization theory, the Karush-Kuhn-Tucker (KKT) optimality conditions for constrained optimization problems with inequality constraints play an essential role. The situation becomes challenging when the theory of traditional optimization is discussed under uncertainty. Several researchers have discussed the interval approach to tackle nonlinear optimization uncertainty and derived the optimality conditions. However, there are several realistic situations in which the interval approach is not suitable. This study aims to introduce the Type-2 interval approach to overcome the limitation of the classical interval approach. This study introduces Type-2 interval order relation and Type-2 interval-valued function concepts to derive generalized KKT optimality conditions for constrained optimization problems under uncertain environments. Then, the optimality conditions are discussed for the unconstrained Type-2 interval-valued optimization problem and after that, using these conditions, generalized KKT conditions are derived. Finally, the proposed approach is demonstrated by numerical examples.

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5

Gashaw, Amanu. "Solving Definite Quadratic Bi-Objective Programming Problems by KKT Conditions." Mathematical Modelling and Applications 2, no. 2 (2017): 21. http://dx.doi.org/10.11648/j.mma.20170202.12.

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6

Kien, Bui Trong, Nguyen Van Tuyen, and Jen-Chih Yao. "Second-Order KKT Optimality Conditions for MultiObjective Optimal Control Problems." SIAM Journal on Control and Optimization 56, no. 6 (January 2018): 4069–97. http://dx.doi.org/10.1137/17m1161750.

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7

Ho, Quyen. "Necessary and sufficient KKT optimality conditions in non-convex optimization." Optimization Letters 11, no. 1 (June 25, 2016): 41–46. http://dx.doi.org/10.1007/s11590-016-1054-0.

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8

Wu, Zili. "KKT conditions for weak ⁎ compact convex sets, theorems of the alternative, and optimality conditions." Journal of Functional Analysis 266, no. 2 (January 2014): 693–712. http://dx.doi.org/10.1016/j.jfa.2013.10.023.

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9

Dempe, Stephan, and Alain B. Zemkoho. "KKT Reformulation and Necessary Conditions for Optimality in Nonsmooth Bilevel Optimization." SIAM Journal on Optimization 24, no. 4 (January 2014): 1639–69. http://dx.doi.org/10.1137/130917715.

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10

Flores-Bazán, Fabián, and Giandomenico Mastroeni. "Characterizing FJ and KKT Conditions in Nonconvex Mathematical Programming with Applications." SIAM Journal on Optimization 25, no. 1 (January 2015): 647–76. http://dx.doi.org/10.1137/13094606x.

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11

Bergmann, Ronny, and Roland Herzog. "Intrinsic Formulation of KKT Conditions and Constraint Qualifications on Smooth Manifolds." SIAM Journal on Optimization 29, no. 4 (January 2019): 2423–44. http://dx.doi.org/10.1137/18m1181602.

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12

Koushki, Javad, and Majid Soleimani-damaneh. "Characterization of generalized FJ and KKT conditions in nonsmooth nonconvex optimization." Journal of Global Optimization 76, no. 2 (November 2, 2019): 407–31. http://dx.doi.org/10.1007/s10898-019-00847-1.

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13

Zheng, Xi Yin, and Kung Fu Ng. "Strong KKT conditions and weak sharp solutions in convex-composite optimization." Mathematical Programming 126, no. 2 (April 17, 2009): 259–79. http://dx.doi.org/10.1007/s10107-009-0277-6.

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14

Wang, Hui, Nazim Agoulmine, Maode Ma, Yajun Li, and Xiaomin Wang. "Network Lifetime Optimization by KKT Optimality Conditions in Wireless Sensor Networks." Wireless Personal Communications 49, no. 2 (August 21, 2008): 179–96. http://dx.doi.org/10.1007/s11277-008-9565-3.

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15

Liu, Hai-Lin, and Qiang Wang. "A Resource Allocation Evolutionary Algorithm for OFDM Based on Karush-Kuhn-Tucker Conditions." Mathematical Problems in Engineering 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/406143.

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For orthogonal frequency division multiplexing (OFDM), resource scheduling plays an important role. In resource scheduling, power allocation and subcarrier allocation are not independent. So the conventional two-step method is not very good for OFDM resource allocation. This paper proposes a new method for OFDM resource allocation. This method combines evolutionary algorithm (EA) with Karush-Kuhn-Tucker conditions (KKT conditions). In the optimizing process, a set of subcarrier allocation programs are made as a population of evolutionary algorithm. For each subcarrier allocation program, a power allocation program is calculated through KKT conditions. Then, the system rate of each subcarrier allocation program can be calculated. The fitness of each individual is its system rate. The information of optimizing subcarrier and power allocation can be interacted with each other. So, it can overcome the shortcoming of the two-step method. Computer experiments show the proposed algorithm is effective.

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16

Liu, Xiao, Tao Jiang, and Hao-hao Li. "Weak optimal inverse problems of interval linear programming based on KKT conditions." Applied Mathematics-A Journal of Chinese Universities 36, no. 3 (September 2021): 462–74. http://dx.doi.org/10.1007/s11766-021-4324-2.

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AbstractIn this paper, weak optimal inverse problems of interval linear programming (IvLP) are studied based on KKT conditions. Firstly, the problem is precisely defined. Specifically, by adjusting the minimum change of the current cost coefficient, a given weak solution can become optimal. Then, an equivalent characterization of weak optimal inverse IvLP problems is obtained. Finally, the problem is simplified without adjusting the cost coefficient of null variable.

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17

Shen, Rui, Zhiqing Meng, and Min Jiang. "Smoothing Partially Exact Penalty Function of Biconvex Programming." Asia-Pacific Journal of Operational Research 37, no. 04 (July 24, 2020): 2040018. http://dx.doi.org/10.1142/s0217595920400187.

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In this paper, a smoothing partial exact penalty function of biconvex programming is studied. First, concepts of partial KKT point, partial optimum point, partial KKT condition, partial Slater constraint qualification and partial exactness are defined for biconvex programming. It is proved that the partial KKT point is equal to the partial optimum point under the condition of partial Slater constraint qualification and the penalty function of biconvex programming is partially exact if partial KKT condition holds. We prove the error bounds properties between smoothing penalty function and penalty function of biconvex programming when the partial KKT condition holds, as well as the error bounds between objective value of a partial optimum point of smoothing penalty function problem and its [Formula: see text]-feasible solution. So, a partial optimum point of the smoothing penalty function optimization problem is an approximately partial optimum point of biconvex programming. Second, based on the smoothing penalty function, two algorithms are presented for finding a partial optimum or approximate [Formula: see text]-feasible solution to an inequality constrained biconvex optimization and their convergence is proved under some conditions. Finally, numerical experiments show that a satisfactory approximate solution can be obtained by the proposed algorithm.

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18

Xiao, Yi-Bin, Nguyen Van Tuyen, Jen-Chih Yao, and Ching-Feng Wen. "Locally Lipschitz vector optimization problems: second-order constraint qualifications, regularity condition and KKT necessary optimality conditions." Positivity 24, no. 2 (June 1, 2019): 313–37. http://dx.doi.org/10.1007/s11117-019-00679-z.

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19

Gupta, Rekha, and Manjari Srivastava. "Constraint qualifications in nonsmooth multiobjective optimization problem." Filomat 31, no. 3 (2017): 781–97. http://dx.doi.org/10.2298/fil1703781g.

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A multiobjective optimization problem (MOP) with inequality and equality constraints is considered where the objective and inequality constraint functions are locally Lipschitz and equality constraint functions are differentiable. Burachik and Rizvi [J. Optim. Theory Appl. 155, 477-491 (2012)] gave Guignard and generalized Abadie regularity conditions for a differentiable programming problem and derived Karush-Kuhn-Tucker (KKT) type necessary optimality conditions. In this paper, we have defined the nonsmooth versions of Guignard and generalized Abadie regularity conditions given by Burachik and Rizvi and obtained KKT necessary optimality conditions for efficient and weak efficient solutions of (MOP). Further several constraint qualifications sufficient for the above newly defined constraint qualifications are introduced for (MOP) with no equality constraints. Relationships between them are presented and examples are constructed to support the results.

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20

Dreves, Axel, Francisco Facchinei, Christian Kanzow, and Simone Sagratella. "On the solution of the KKT conditions of generalized Nash equilibrium problems." SIAM Journal on Optimization 21, no. 3 (July 2011): 1082–108. http://dx.doi.org/10.1137/100817000.

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21

Singh, D., B. A. Dar, and D. S. Kim. "KKT optimality conditions in interval valued multiobjective programming with generalized differentiable functions." European Journal of Operational Research 254, no. 1 (October 2016): 29–39. http://dx.doi.org/10.1016/j.ejor.2016.03.042.

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22

Zhang, Tianyu, and Liwei Zhang. "Critical Multipliers in Semidefinite Programming." Asia-Pacific Journal of Operational Research 37, no. 04 (May 19, 2020): 2040012. http://dx.doi.org/10.1142/s0217595920400126.

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It was proved in Izmailov and Solodov (2014). Newton-Type Methods for Optimization and Variational Problems, Springer] that the existence of a noncritical multiplier for a (smooth) nonlinear programming problem is equivalent to an error bound condition for the Karush–Kuhn–Thcker (KKT) system without any assumptions. This paper investigates whether this result still holds true for a (smooth) nonlinear semidefinite programming (SDP) problem. The answer is negative: the existence of noncritical multiplier does not imply the error bound condition for the KKT system without additional conditions, which is illustrated by an example. In this paper, we obtain characterizations, in terms of the problem data, the critical and noncritical multipliers for a SDP problem. We prove that, for the SDP problem, the noncriticality property can be derived from the error bound condition for the KKT system without any assumptions, and we give an example to show that the noncriticality does not imply the error bound for the KKT system. We propose a set of assumptions under which the error bound condition for the KKT system can be derived from the noncriticality property. a Finally, we establish a new error bound for [Formula: see text]-part, which is expressed by both perturbation and the multiplier estimation.

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23

Yu, Nanxiang, and Dong Qiu. "The Karush-Kuhn-Tucker Optimality Conditions for the Fuzzy Optimization Problems in the Quotient Space of Fuzzy Numbers." Complexity 2017 (2017): 1–8. http://dx.doi.org/10.1155/2017/1242841.

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We propose the solution concepts for the fuzzy optimization problems in the quotient space of fuzzy numbers. The Karush-Kuhn-Tucker (KKT) optimality conditions are elicited naturally by introducing the Lagrange function multipliers. The effectiveness is illustrated by examples.

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24

Jiang, Ai Ping, and Feng Wen Huang. "QP-Free Method for Nonlinear Programming Problems." Key Engineering Materials 467-469 (February 2011): 882–87. http://dx.doi.org/10.4028/www.scientific.net/kem.467-469.882.

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In this paper, A QP-free feasible method was proposed to obtain the local convergence under some weaker conditions for the minimization of a smooth function subject to smooth inequalities. Based on the solutions of linear systems of equation reformulation of the KKT optimality conditions, this method uses the 3-1 NCP function[1].The method is iterative, which means each iteration can be viewed as a perturbation of a Newton or Quasi Newton on both the primal and dual variables for the solution of the equalities in the KKT first order conditions of optimality, and the feasibility of all iterations is ensured in this method. In particular, this method is implementable and globally convergent without assuming the strict complementarity condition, the isolation of the accumulation point and the linear independence of the gradients of active constrained functions. The method has also superlinear convergence rate under some mild conditions.

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25

Barilla, D., G. Caristi, and A. Puglisi. "Optimality Conditions for Nondifferentiable Multiobjective Semi-Infinite Programming Problems." Abstract and Applied Analysis 2016 (2016): 1–6. http://dx.doi.org/10.1155/2016/5367190.

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We have considered a multiobjective semi-infinite programming problem with a feasible set defined by inequality constraints. First we studied a Fritz-John type necessary condition. Then, we introduced two constraint qualifications and derive the weak and strong Karush-Kuhn-Tucker (KKT in brief) types necessary conditions for an efficient solution of the considered problem. Finally an extension of a Caristi-Ferrara-Stefanescu result for the (Φ,ρ)-invexity is proved, and some sufficient conditions are presented under this weak assumption. All results are given in terms of Clark subdifferential.

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26

Sharma, Sunila, and Priyanka Yadav. "Nonsmooth Vector Optimization Problem Involving Second-Order Semipseudo, Semiquasi Cone-Convex Functions." Statistics, Optimization & Information Computing 9, no. 2 (September 26, 2020): 383–98. http://dx.doi.org/10.19139/soic-2310-5070-839.

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Recently, Suneja et al. [26] introduced new classes of second-order cone-(η; ξ)-convex functions along with theirgeneralizations and used them to prove second-order Karush–Kuhn–Tucker (KKT) type optimality conditions and duality results for the vector optimization problem involving first-order differentiable and second-order directionally differentiable functions. In this paper, we move one step ahead and study a nonsmooth vector optimization problem wherein the functions involved are first and second-order directionally differentiable. We introduce new classes of nonsmooth second-order cone-semipseudoconvex and nonsmooth second-order cone-semiquasiconvex functions in terms of second-order directional derivatives. Second-order KKT type sufficient optimality conditions and duality results for the same problem are proved using these functions.

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27

Li, Mengmou. "Generalized Lagrange Multiplier Method and KKT Conditions With an Application to Distributed Optimization." IEEE Transactions on Circuits and Systems II: Express Briefs 66, no. 2 (February 2019): 252–56. http://dx.doi.org/10.1109/tcsii.2018.2842085.

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28

Tung, Le Thanh. "Strong Karush–Kuhn–Tucker optimality conditions for multiobjective semi-infinite programming via tangential subdifferential." RAIRO - Operations Research 52, no. 4-5 (October 2018): 1019–41. http://dx.doi.org/10.1051/ro/2018020.

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The main aim of this paper is to study strong Karush–Kuhn–Tucker (KKT) optimality conditions for nonsmooth multiobjective semi-infinite programming (MSIP) problems. By using tangential subdifferential and suitable regularity conditions, we establish some strong necessary optimality conditions for some types of efficient solutions of nonsmooth MSIP problems. In addition to the theoretical results, some examples are provided to illustrate the advantages of our outcomes.

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29

Hassan, Mansur, and Adam Baharum. "Modified Courant-Beltrami penalty function and a duality gap for invex optimization problem." International Journal for Simulation and Multidisciplinary Design Optimization 10 (2019): A10. http://dx.doi.org/10.1051/smdo/2019010.

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In this paper, we modified a Courant-Beltrami penalty function method for constrained optimization problem to study a duality for convex nonlinear mathematical programming problems. Karush-Kuhn-Tucker (KKT) optimality conditions for the penalized problem has been used to derived KKT multiplier based on the imposed additional hypotheses on the constraint function g. A zero-duality gap between an optimization problem constituted by invex functions with respect to the same function η and their Lagrangian dual problems has also been established. The examples have been provided to illustrate and proved the result for the broader class of convex functions, termed invex functions.

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30

Das, Koushik, and Chandal Nahak. "Set-valued optimization problems via second-order contingent epiderivative." Yugoslav Journal of Operations Research, no. 00 (2020): 41. http://dx.doi.org/10.2298/yjor191215041d.

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In this paper, we establish second-order KKT conditions of a set-valued optimization problem and study second-order Mond-Weir, Wolfe, and mixed types duals with the help of second-order contingent epiderivative and second-order generalized cone convexity assumptions.

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31

KERDKAEW, JUTAMAS, RABIAN WANGKEEREE, and GUE MYUNG LEE. "On optimality conditions for robust weak sharp solution in uncertain optimizations." Carpathian Journal of Mathematics 36, no. 3 (September 30, 2020): 443–52. http://dx.doi.org/10.37193/cjm.2020.03.12.

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In this paper, we investigate the robust optimization problem involving nonsmooth and nonconvex real-valued functions. We firstly establish a necessary condition for the local robust weak sharp solution of considered problem under a constraint qualification. These optimality conditions are presented in terms of multipliers and Mordukhovich subdifferentials of the related functions. Then, by employing the robust version of the (KKT) condition, and some appropriate generalized convexity conditions, we also obtain some sufficient conditions for the global robust weak sharp solutions of the problem. In addition, some examples are presented for illustrating or supporting the results.

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32

Ahmad, Izhar, Deepak Singh, and Bilal Dar. "Optimality conditions for invex interval valued nonlinear programming problems involving generalized H-derivative." Filomat 30, no. 8 (2016): 2121–38. http://dx.doi.org/10.2298/fil1608121a.

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In this paper, some interval valued programming problems are discussed. The solution concepts are adopted from Wu [7] and Chalco-Cano et al. [34]. By considering generalized Hukuhara differentiability and generalized convexity (viz. ?-preinvexity, ?-invexity etc.) of interval valued functions, the KKT optimality conditions for obtaining (LS and LU) optimal solutions are elicited by introducing Lagrangian multipliers. Our results generalize the results of Wu [7], Zhang et al. [11] and Chalco-Cano et al. [34]. To illustrate our theorems suitable examples are also provided

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33

Gadhi, Nazih Abderrazzak, and Lahoussine Lafhim. "Optimality conditions for a bilevel optimization problem in terms of KKT multipliers and convexificators." Croatian Operational Research Review 10, no. 2 (December 13, 2019): 329–35. http://dx.doi.org/10.17535/crorr.2019.0026.

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34

Gulliksson, M. "KKT Conditions for Rank-Deficient Nonlinear Least-Square Problems with Rank-Deficient Nonlinear Constraints." Journal of Optimization Theory and Applications 100, no. 1 (January 1999): 145–60. http://dx.doi.org/10.1023/a:1021721132282.

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35

Birgin, E. G., J. L. Gardenghi, J. M. Martínez, S. A. Santos, and Ph L. Toint. "Evaluation Complexity for Nonlinear Constrained Optimization Using Unscaled KKT Conditions and High-Order Models." SIAM Journal on Optimization 26, no. 2 (January 2016): 951–67. http://dx.doi.org/10.1137/15m1031631.

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36

Börgens, Eike, Christian Kanzow, Patrick Mehlitz, and Gerd Wachsmuth. "New Constraint Qualifications for Optimization Problems in Banach Spaces Based on Asymptotic KKT Conditions." SIAM Journal on Optimization 30, no. 4 (January 2020): 2956–82. http://dx.doi.org/10.1137/19m1306804.

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37

Kanzi, N. "On strong KKT optimality conditions for multiobjective semi-infinite programming problems with Lipschitzian data." Optimization Letters 9, no. 6 (September 26, 2014): 1121–29. http://dx.doi.org/10.1007/s11590-014-0801-3.

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38

Englert, Peter, Ngo Anh Vien, and Marc Toussaint. "Inverse KKT: Learning cost functions of manipulation tasks from demonstrations." International Journal of Robotics Research 36, no. 13-14 (December 2017): 1474–88. http://dx.doi.org/10.1177/0278364917745980.

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Inverse optimal control (IOC) assumes that demonstrations are the solution to an optimal control problem with unknown underlying costs, and extracts parameters of these underlying costs. We propose the framework of inverse Karush–Kuhn–Tucker (KKT), which assumes that the demonstrations fulfill the KKT conditions of an unknown underlying constrained optimization problem, and extracts parameters of this underlying problem. Using this we can exploit the latter to extract the relevant task spaces and parameters of a cost function for skills that involve contacts. For a typical linear parameterization of cost functions this reduces to a quadratic program, ensuring guaranteed and very efficient convergence, but we can deal also with arbitrary non-linear parameterizations of cost functions. We also present a non-parametric variant of inverse KKT that represents the cost function as a functional in reproducing kernel Hilbert spaces. The aim of our approach is to push learning from demonstration to more complex manipulation scenarios that include the interaction with objects and therefore the realization of contacts/constraints within the motion. We demonstrate the approach on manipulation tasks such as sliding a box, closing a drawer and opening a door.

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39

Guo, Ye, Zhao, and Liu. "gH-Symmetrically Derivative of Interval-Valued Functions and Applications in Interval-Valued Optimization." Symmetry 11, no. 10 (September 25, 2019): 1203. http://dx.doi.org/10.3390/sym11101203.

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In this paper, we present the gH-symmetrical derivative of interval-valued functions andits properties. In application, we apply this new derivative to investigate the Karush–Kuhn–Tucker(KKT) conditions of interval-valued optimization problems. Meanwhile, some examples are workedout to illuminate the obtained results.

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40

Wu, Ruei-Shing, and Chuei-Tin Chang. "Development of mathematical programs for evaluating dynamic and temporal flexibility indices based on KKT conditions." Journal of the Taiwan Institute of Chemical Engineers 73 (April 2017): 86–92. http://dx.doi.org/10.1016/j.jtice.2016.09.009.

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41

Cánovas, M. J., A. Hantoute, M. A. López, and J. Parra. "Stability of Indices in the KKT Conditions and Metric Regularity in Convex Semi-Infinite Optimization." Journal of Optimization Theory and Applications 139, no. 3 (April 30, 2008): 485–500. http://dx.doi.org/10.1007/s10957-008-9407-1.

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42

Ali, Zuhura J., Nor K. Noordin, Aduwati Sali, Fazirulhisyam Hashim, and Mohammed Balfaqih. "Novel Resource Allocation Techniques for Downlink Non-Orthogonal Multiple Access Systems." Applied Sciences 10, no. 17 (August 26, 2020): 5892. http://dx.doi.org/10.3390/app10175892.

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Non-orthogonal multiple access (NOMA) plays an important role in achieving high capacity for fifth-generation (5G) networks. Efficient resource allocation is vital for NOMA system performance to maximize the sum rate and energy efficiency. In this context, this paper proposes optimal solutions for user pairing and power allocation to maximize the system sum rate and energy efficiency performance. We identify the power allocation problem as a nonconvex constrained problem for energy efficiency maximization. The closed-form solutions are derived using Karush–Kuhn–Tucker (KKT) conditions for maximizing the system sum rate and the Dinkelbach (DKL) algorithm for maximizing system energy efficiency. Moreover, the Hungarian (HNG) algorithm is utilized for pairing two users with different channel condition circumstances. The results show that with 20 users, the sum rate of the proposed NOMA with optimal power allocation using KKT conditions and HNG (NOMA-PKKT-HNG) is 6.7% higher than that of NOMA with difference of convex programming (NOMA-DC). The energy efficiency with optimal power allocation using DKL and HNG (NOMA-PDKL-HNG) is 66% higher than when using NOMA-DC.

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43

Das, Koushik. "Sufficiency and duality of set-valued fractional programming problems via second-order contingent epiderivative." Yugoslav Journal of Operations Research, no. 00 (2021): 19. http://dx.doi.org/10.2298/yjor210218019d.

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In this paper, we establish second-order sufficient KKT optimality conditions of a set-valued fractional programming problem under second-order generalized cone convexity assumptions. We also prove duality results between the primal problem and second-order dual problems of parametric, Mond-Weir, Wolfe, and mixed types via the notion of second-order contingent epiderivative.

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44

Abdelilah, Makrizi, and BouchaÃ¯b Radi. "SOLUTION OF THE LARGE MINIMUM COMPLIANCE PROBLEM USING BILEVEL OPTIMIZATION." JOURNAL OF ADVANCES IN MATHEMATICS 12, no. 2 (April 15, 2016): 5928–37. http://dx.doi.org/10.24297/jam.v12i2.556.

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The topology optimization problem have a great industrial interest. Using the subdomains method, we have formulated the decomposed topology optimization problem as a bilevel one. In this paper, we reformulate our bilevel problem as a single level optimization problem by replacing the lower level optimization problem with its KKT optimality conditions, we give also a new algorithm and numerical results.

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45

Keerthi, S. S., S. K. Shevade, C. Bhattacharyya, and K. R. K. Murthy. "Improvements to Platt's SMO Algorithm for SVM Classifier Design." Neural Computation 13, no. 3 (March 1, 2001): 637–49. http://dx.doi.org/10.1162/089976601300014493.

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This article points out an important source of inefficiency in Platt's sequential minimal optimization (SMO) algorithm that is caused by the use of a single threshold value. Using clues from the KKT conditions for the dual problem, two threshold parameters are employed to derive modifications of SMO. These modified algorithms perform significantly faster than the original SMO on all benchmark data sets tried.

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46

Nguyen Dinh, Huy, Tinh Cao Thanh, Tung Nguyen, and Oanh Cao Thi Be. "Necessary optimality conditions in nonsmooth semi-infinite multiobjective optimization under metric subregularity." Science & Technology Development Journal - Engineering and Technology 3, SI3 (January 22, 2021): SI52—SI57. http://dx.doi.org/10.32508/stdjet.v3isi3.637.

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We consider nonsmooth semi-infinite multiobjective optimization problems under mixed constraints, including infinitely many mixed constraints by using Clarke subdifferential. Semi-infinite programming (SIP) is the minimization of many scalar objective functions subject to a possibly infinite system of inequality or/and equality constraints. SIPs have been proved to be very important in optimization and applications. Semi-infinite programming problems arise in various fields of engineering such as control systems design, decision making under competition, and multiobjective optimization. There is extensive literature on standard semi-infinite programming problems. The investigation of optimality conditions for these problems is always one of the most attractive topics and has been studied extensively in the literature. In our work, we study optimality conditions for weak efficiency of a multiobjective semi-infinite optimization problem under mixed constraints including infinitely many of both equality and inequality constraints in terms of Clarke subdifferential. Our conditions are the form of the Karush-Kuhn-Tucker (KKT) multiplier. To the best of our knowledge, only a few papers are dealing with optimality conditions for SIPs subject to mixed constraints. By the Pshenichnyi-Levin-Valadire (PLV) property and the directional metric subregularity, we introduce a type of Mangasarian-Fromovitz constraint qualification (MFCQ). Then we show that (MFCQ) is a sufficient condition to guarantee the extended Abadie constraint qualification (ACQ) to satisfy. In our constraint qualifications, all functions are nonsmooth and the number of constraints is not necessarily finite. In our paper, we do not need the involved functions: convexity and differentiability. Later, we apply the extended Abadie constraint qualification to get the KKT multipliers for weak efficient solutions of SIP. Many examples are provided to illustrate some advantages of our results. The paper is organized as follows. In Section Preliminaries, we present our basic definitions of nonsmooth and convex analysis. Section Main Results prove necessary conditions for the weakly efficient solution in terms of the Karush-Kuhn-Tucker mult iplier rule with the help of some constraint qualifications.

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Aris, Muhammad, and Sudirto Malan. "BAKTERI PATOGEN PADA KEPITING KELAPA (Birgus latro)." JURNAL PERIKANAN TROPIS 8, no. 1 (June 3, 2021): 57. http://dx.doi.org/10.35308/jpt.v8i1.2555.

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Coconut crab (Birgus latro) is a fishery resource with high economic value. Coconut Crab is only found in eastern Indonesia, covering Sulawesi, Maluku and North Maluku. One of the habitat of Coconut Crab in North Maluku is Moor Island, Central Halmahera. The coastal typology of this island is predominantly rocky with many gaps and small caves, as well as several steep slopes with dominant vegetation conditions of coconut, beach pandanus and other coastal plants. Walnut Crab is often used as a consumption ingredient because it has delicious taste and high nutritions. However, the use of crustaceans for consumption can also be dangerous. This is because crustaceans also contain several pathogenic bacteria. This study aimed to identify pathogenic bacteria isolated from Coconut Crab which is the largest crustacean in the world. 5 samples of Coconut Crab were taken from Moor Island. Isolated samples marked KK1, KK2, KK3, KK4 and KK5. Pure bacterial isolates were obtained from Coconut Crab samples, evaluated for colony type and identified based on biochemical characterization. The types of pathogenic bacteria identified in samples KK1, KK2, KK3, KK4 and KK5 were Escherichia coli, Pseudomonas sp. and Staphylococcus sp.

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Chalco-Cano, Y., W. A. Lodwick, and A. Rufian-Lizana. "Optimality conditions of type KKT for optimization problem with interval-valued objective function via generalized derivative." Fuzzy Optimization and Decision Making 12, no. 3 (February 21, 2013): 305–22. http://dx.doi.org/10.1007/s10700-013-9156-y.

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Cárcamo, Gabriel, and Fabián Flores-Bazán. "Strong duality and KKT conditions in nonconvex optimization with a single equality constraint and geometric constraint." Mathematical Programming 168, no. 1-2 (October 15, 2016): 369–400. http://dx.doi.org/10.1007/s10107-016-1078-3.

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Ruiz-Garzón, Gabriel, Jaime Ruiz-Zapatero, Rafaela Osuna-Gómez, and Antonio Rufián-Lizana. "Necessary and Sufficient Second-Order Optimality Conditions on Hadamard Manifolds." Mathematics 8, no. 7 (July 14, 2020): 1152. http://dx.doi.org/10.3390/math8071152.

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This work is intended to lead a study of necessary and sufficient optimality conditions for scalar optimization problems on Hadamard manifolds. In the context of this geometry, we obtain and present new function types characterized by the property of having all their second-order stationary points be global minimums. In order to do so, we extend the concept convexity in Euclidean space to a more general notion of invexity on Hadamard manifolds. This is done employing notions of second-order directional derivatives, second-order pseudoinvexity functions, and the second-order Karush–Kuhn–Tucker-pseudoinvexity problem. Thus, we prove that every second-order stationary point is a global minimum if and only if the problem is either second-order pseudoinvex or second-order KKT-pseudoinvex depending on whether the problem regards unconstrained or constrained scalar optimization, respectively. This result has not been presented in the literature before. Finally, examples of these new characterizations are provided in the context of “Higgs Boson like” potentials, among others.

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