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Journal articles on the topic 'Karush-Kuhn-Tucker conditions'

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Published: 4 June 2021

Last updated: 4 February 2022

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1

Pan, Shaohua, Shujun Bi, and Jein-Shan Chen. "Nonsingularity Conditions for FB System of Reformulating Nonlinear Second-Order Cone Programming." Abstract and Applied Analysis 2013 (2013): 1–21. http://dx.doi.org/10.1155/2013/602735.

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This paper is a counterpart of Bi et al., 2011. For a locally optimal solution to the nonlinear second-order cone programming (SOCP), specifically, under Robinson’s constraint qualification, we establish the equivalence among the following three conditions: the nonsingularity of Clarke’s Jacobian of Fischer-Burmeister (FB) nonsmooth system for the Karush-Kuhn-Tucker conditions, the strong second-order sufficient condition and constraint nondegeneracy, and the strong regularity of the Karush-Kuhn-Tucker point.

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2

Jahn, Johannes. "Karush–Kuhn–Tucker Conditions in Set Optimization." Journal of Optimization Theory and Applications 172, no. 3 (January 30, 2017): 707–25. http://dx.doi.org/10.1007/s10957-017-1066-7.

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3

Chen, Han, and Pasquale Malacaria. "Studying Maximum Information Leakage Using Karush-Kuhn-Tucker Conditions." Electronic Proceedings in Theoretical Computer Science 7 (October 23, 2009): 1–15. http://dx.doi.org/10.4204/eptcs.7.1.

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4

Khanh, Phan Quoc, and Nguyen Minh Tung. "Higher-Order Karush--Kuhn--Tucker Conditions in Nonsmooth Optimization." SIAM Journal on Optimization 28, no. 1 (January 2018): 820–48. http://dx.doi.org/10.1137/16m1079920.

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5

Kim, Do Sang, and Nguyen Van Tuyen. "A note on second-order Karush–Kuhn–Tucker necessary optimality conditions for smooth vector optimization problems." RAIRO - Operations Research 52, no. 2 (April 2018): 567–75. http://dx.doi.org/10.1051/ro/2017026.

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6

Abdulaleem, Najeeb. "E-invexity and generalized E-invexity in E-differentiable multiobjective programming." ITM Web of Conferences 24 (2019): 01002. http://dx.doi.org/10.1051/itmconf/20192401002.

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In this paper, a new concept of generalized convexity is introduced for not necessarily diﬀerentiable vector optimization problems. For an E-diﬀerentiable function, the concept of E-invexity is introduced as a generalization of the E-diﬀerentiable E-convexity notion. In addition, some properties of E-diﬀerentiable E-invex functions are investigated. Furthermore, the so-called E-Karush-Kuhn-Tucker necessary optimality conditions are established for the considered E-diﬀerentiable vector optimization problems with both inequality and equality constraints. Also, the suﬃciency of the E-Karush-Kuhn-Tucker necessary optimality conditions are proved for such E-diﬀerentiable vector optimization problems in which the involved functions are E-invex and/or generalized E-invex.

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7

Luu, Do Van, and Tran Van Su. "Contingent derivatives and necessary efficiency conditions for vector equilibrium problems with constraints." RAIRO - Operations Research 52, no. 2 (April 2018): 543–59. http://dx.doi.org/10.1051/ro/2017042.

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We establish Fritz John necessary conditions for local weak efficient solutions of vector equilibrium problems with constraints in terms of contingent derivatives. Under suitable constraint qualifications, Karush–Kuhn–Tucker necessary conditions for those solutions are investigated.

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8

Antczak, Tadeusz. "Multiobjective programming under nondifferentiable G-V-invexity." Filomat 30, no. 11 (2016): 2909–23. http://dx.doi.org/10.2298/fil1611909a.

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In the paper, new Fritz John type necessary optimality conditions and new Karush-Kuhn-Tucker type necessary opimality conditions are established for the considered nondifferentiable multiobjective programming problem involving locally Lipschitz functions. Proofs of them avoid the alternative theorem usually applied in such a case. The sufficiency of the introduced Karush-Kuhn-Tucker type necessary optimality conditions are proved under assumptions that the functions constituting the considered nondifferentiable multiobjective programming problem are G-V-invex with respect to the same function ?. Further, the so-called nondifferentiable vector G-Mond-Weir dual problem is defined for the considered nonsmooth multiobjective programming problem. Under nondifferentiable G-V-invexity hypotheses, several duality results are established between the primal vector optimization problem and its G-dual problem in the sense of Mond-Weir.

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9

Haeser, Gabriel, and Alberto Ramos. "Constraint Qualifications for Karush–Kuhn–Tucker Conditions in Multiobjective Optimization." Journal of Optimization Theory and Applications 187, no. 2 (September 29, 2020): 469–87. http://dx.doi.org/10.1007/s10957-020-01749-z.

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10

Chalco-Cano, Y., W. A. Lodwick, R. Osuna-Gómez, and A. Rufián-Lizana. "The Karush–Kuhn–Tucker optimality conditions for fuzzy optimization problems." Fuzzy Optimization and Decision Making 15, no. 1 (April 23, 2015): 57–73. http://dx.doi.org/10.1007/s10700-015-9213-9.

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11

Alavi Hejazi, Mansoureh. "On Approximate Karush–Kuhn–Tucker Conditions for Multiobjective Optimization Problems." Iranian Journal of Science and Technology, Transactions A: Science 42, no. 2 (March 17, 2017): 873–79. http://dx.doi.org/10.1007/s40995-017-0241-x.

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12

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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13

Monte, Moisés Rodrigues Cirilo, and Valeriano Antunes De Oliveira. "A Full Rank Condition for Continuous-Time Optimization Problems with Equality and Inequality Constraints." TEMA (São Carlos) 20, no. 1 (May 20, 2019): 15. http://dx.doi.org/10.5540/tema.2019.020.01.15.

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First and second order necessary optimality conditions of Karush-Kuhn-Tucker type are established for continuous-time optimization problems with equality and inequality constraints. A full rank type regularity condition along with an uniform implicit function theorem are used in order to achieve such necessary conditions.

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14

Cornaciu, Veronica, and Ileana Ioana. "The Avriel-Ben-Tal algebraic operations approach for a short version proof of the Karush-Kuhn-Tucker optimality conditions." Analele Universitatii "Ovidius" Constanta - Seria Matematica 25, no. 2 (July 26, 2017): 39–48. http://dx.doi.org/10.1515/auom-2017-0019.

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AbstractIn this paper, by using (h, ϕ)-generalized directional derivative and (h, ϕ)-generalized gradient, the authors directly derives the Karush- Kuhn-Tucker conditions by applying a corollary of Farkas lemma under the Mangasarian-Fromovitz constraint qualification.Furthermore, the boundedness of Lagrange multipliers is showed.

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15

Ye, Jane J., and Jin Zhang. "Enhanced Karush–Kuhn–Tucker Conditions for Mathematical Programs with Equilibrium Constraints." Journal of Optimization Theory and Applications 163, no. 3 (December 3, 2013): 777–94. http://dx.doi.org/10.1007/s10957-013-0493-3.

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16

Tuyen, Nguyen Van, Nguyen Quang Huy, and Do Sang Kim. "Strong second-order Karush–Kuhn–Tucker optimality conditions for vector optimization." Applicable Analysis 99, no. 1 (June 26, 2018): 103–20. http://dx.doi.org/10.1080/00036811.2018.1489956.

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17

Zhu, S. K., S. J. Li, and K. L. Teo. "Second-order Karush–Kuhn–Tucker optimality conditions for set-valued optimization." Journal of Global Optimization 58, no. 4 (April 10, 2013): 673–92. http://dx.doi.org/10.1007/s10898-013-0067-9.

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18

Huy, Nguyen Quang, Do Sang Kim, and Nguyen Van Tuyen. "New Second-Order Karush–Kuhn–Tucker Optimality Conditions for Vector Optimization." Applied Mathematics & Optimization 79, no. 2 (June 20, 2017): 279–307. http://dx.doi.org/10.1007/s00245-017-9432-2.

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19

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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20

Kiefer, Bjoern, Tobias Waffenschmidt, Leon Sprave, and Andreas Menzel. "A gradient-enhanced damage model coupled to plasticity—multi-surface formulation and algorithmic concepts." International Journal of Damage Mechanics 27, no. 2 (January 5, 2017): 253–95. http://dx.doi.org/10.1177/1056789516676306.

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A non-local gradient-enhanced damage-plasticity formulation is proposed, which prevents the loss of well-posedness of the governing field equations in the post-critical damage regime. The non-locality of the formulation then manifests itself in terms of a non-local free energy contribution that penalizes the occurrence of damage gradients. A second penalty term is introduced to force the global damage field to coincide with the internal damage state variable at the Gauss point level. An enforcement of Karush–Kuhn–Tucker conditions on the global level can thus be avoided and classical local damage models may directly be incorporated and equipped with a non-local gradient enhancement. An important part of the present work is to investigate the efficiency and robustness of different algorithmic schemes to locally enforce the Karush–Kuhn–Tucker conditions in the multi-surface damage-plasticity setting. Response simulations for representative inhomogeneous boundary value problems are studied to assess the effectiveness of the gradient enhancement regarding stability and mesh objectivity.

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21

Tran, Thach Van, and Son Quang Ta. "ALMOST e - QUASISOLUTIONS OF A NONCONVEX PROGRAMMING PROBLEM WITH AN INFINITE NUMBER OF CONSTRAINTS." Science and Technology Development Journal 15, no. 3 (September 30, 2012): 57–68. http://dx.doi.org/10.32508/stdj.v15i3.1847.

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Under a generalized Karush – Kuhn – Tucker condition up to e, we establish some sufficient optimality conditions for almost e- quasisolutions of a nonconvex programming problem which has an infinite number of constraints. Some results on -weak duality in Mond-Weir type for the problem are also introduced

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22

Le, Thanh. "Karush-Kuhn-Tucker optimality conditions and duality for multiobjective semi-infinite programming with equilibrium constraints." Yugoslav Journal of Operations Research, no. 00 (2020): 24. http://dx.doi.org/10.2298/yjor200117024l.

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The purpose of this paper is to study multiobjective semi-infinite programming with equilibrium constraints. Firstly, the necessary and sufficient Karush-Kuhn-Tucker optimality conditions for multiobjective semi-infinite programming with equilibrium constraints are established. Then, we formulate types of Wolfe and Mond-Weir dual problems and investigate duality relations under convexity assumptions. Some examples are given to verify our results.

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23

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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24

Ito, Kazufumi, and Karl Kunisch. "Karush–Kuhn–Tucker Conditions for Nonsmooth Mathematical Programming Problems in Function Spaces." SIAM Journal on Control and Optimization 49, no. 5 (January 2011): 2133–54. http://dx.doi.org/10.1137/100817061.

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25

Tapia, R. A., and M. W. Trosset,. "An Extension of the Karush–Kuhn–Tucker Necessity Conditions to Infinite Programming." SIAM Review 36, no. 1 (March 1994): 1–17. http://dx.doi.org/10.1137/1036001.

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26

Clempner, Julio B. "Necessary and sufficient Karush–Kuhn–Tucker conditions for multiobjective Markov chains optimality." Automatica 71 (September 2016): 135–42. http://dx.doi.org/10.1016/j.automatica.2016.04.044.

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27

Zhang, Jianke. "Optimality Condition and Wolfe Duality for Invex Interval-Valued Nonlinear Programming Problems." Journal of Applied Mathematics 2013 (2013): 1–11. http://dx.doi.org/10.1155/2013/641345.

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The concepts of preinvex and invex are extended to the interval-valued functions. Under the assumption of invexity, the Karush-Kuhn-Tucker optimality sufficient and necessary conditions for interval-valued nonlinear programming problems are derived. Based on the concepts of having no duality gap in weak and strong sense, the Wolfe duality theorems for the invex interval-valued nonlinear programming problems are proposed in this paper.

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28

Zhao, Jing, and Maojun Bin. "Karush-Kuhn-Tucker optimality conditions for a class of robust optimization problems with an interval-valued objective function." Open Mathematics 18, no. 1 (July 22, 2020): 781–93. http://dx.doi.org/10.1515/math-2020-0042.

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Abstract In this article, we study the nonlinear and nonsmooth interval-valued optimization problems in the face of data uncertainty, which are called interval-valued robust optimization problems (IVROPs). We introduce the concept of nondominated solutions for the IVROP. If the interval-valued objective function f and constraint functions {g}_{i} are nonsmooth on Banach space E, we establish a nonsmooth and robust Karush-Kuhn-Tucker optimality theorem.

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29

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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30

Delgado, Angel Ramon Sanchez, and Sergio Drumond Ventura. "Optimality Conditions of Agricultural Production With Fixed Input Costs." Journal of Agricultural Studies 9, no. 2 (March 8, 2021): 151. http://dx.doi.org/10.5296/jas.v9i2.18389.

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We present a computational procedure to maximize the production of a given agricultural crop with limited inputs (water-nitrogen), and where a fixed cost (or expense) of the inputs (general problem of agricultural production) is imposed. Theoretically the procedure is based on the Karush-Kuhn-Tucker optimality conditions and numerically was tested with three different scenarios defined in the literature, for the cultures: Lettuce, Oats, Onions and Melons. In each agricultural scenario considered, it was possible to verify that the procedure is a reliable alternative in making agribusiness economic decisions.

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31

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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32

Feng, Min, and Shengjie Li. "Second-Order Strong Karush/Kuhn–Tucker Conditions for Proper Efficiencies in Multiobjective Optimization." Journal of Optimization Theory and Applications 181, no. 3 (February 14, 2019): 766–86. http://dx.doi.org/10.1007/s10957-019-01484-0.

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33

Debnath, Indira P., and Shiv K. Gupta. "The Karush–Kuhn–Tucker conditions for multiple objective fractional interval valued optimization problems." RAIRO - Operations Research 54, no. 4 (June 12, 2020): 1161–88. http://dx.doi.org/10.1051/ro/2019055.

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In this article, we focus on a class of a fractional interval multivalued programming problem. For the solution concept, LU-Pareto optimality and LS-Pareto, optimality are discussed, and some nontrivial concepts are also illustrated with small examples. The ideas of LU-V-invex and LS-V-invex for a fractional interval problem are introduced. Using these invexity suppositions, we establish the Karush–Kuhn–Tucker optimality conditions for the problem assuming the functions involved to be gH-differentiable. Non-trivial examples are discussed throughout the manuscript to make a clear understanding of the results established. Results obtained in this paper unify and extend some previously known results appeared in the literature.

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34

Cortez, Cristhian Alberto Celestino, and José Carlos Pinto. "Improvement of Karush–Kuhn–Tucker conditions under uncertainties using robust decision making indexes." Applied Mathematical Modelling 43 (March 2017): 630–46. http://dx.doi.org/10.1016/j.apm.2016.11.021.

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35

Burachik, Regina S., and M. M. Rizvi. "Proper Efficiency and Proper Karush–Kuhn–Tucker Conditions for Smooth Multiobjective Optimization Problems." Vietnam Journal of Mathematics 42, no. 4 (November 7, 2014): 521–31. http://dx.doi.org/10.1007/s10013-014-0102-2.

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36

Van Tuyen, Nguyen, Jen-Chih Yao, and Ching-Feng Wen. "A note on approximate Karush–Kuhn–Tucker conditions in locally Lipschitz multiobjective optimization." Optimization Letters 13, no. 1 (April 9, 2018): 163–74. http://dx.doi.org/10.1007/s11590-018-1261-y.

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37

Yuan, Dehui, and Xiaoling Liu. "Mathematical programming involving (α, p)-right upper-Dini-derivative functions." Filomat 27, no. 5 (2013): 899–908. http://dx.doi.org/10.2298/fil1305899y.

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In this paper, we give some new generalized convexities with the tool-right upper-Dini-derivative which is an extension of directional derivative. Next, we establish not only Karush-Kuhn-Tucker necessary but also sufficient optimality conditions for mathematical programming involving new generalized convex functions. In the end, weak, strong and converse duality results are proved to relate weak Pareto (efficient) solutions of the multi-objective programming problems (VP), (MVD) and (MWD).

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38

Kapoor, Malti, Surjeet K. Suneja, and Sunila Sharma. "Generalized (Phi, Rho)-convexity in nonsmooth vector optimization over cones." An International Journal of Optimization and Control: Theories & Applications (IJOCTA) 6, no. 1 (January 24, 2016): 1–7. http://dx.doi.org/10.11121/ijocta.01.2016.00247.

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In this paper, new classes of cone-generalized (Phi,Rho)-convex functions are introduced for a nonsmooth vector optimization problem over cones, which subsume several known studied classes. Using these generalized functions, various sufficient Karush-Kuhn-Tucker (KKT) type nonsmooth optimality conditions are established wherein Clarke's generalized gradient is used. Further, we prove duality results for both Wolfe and Mond-Weir type duals under various types of cone-generalized (Phi,Rho)-convexity assumptions.Phi,Rho

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39

Tung, Nguyen Minh. "Second-order efficient optimality conditions for set-valued vector optimization in terms of asymptotic contingent epiderivatives." RAIRO - Operations Research 55, no. 2 (March 2021): 841–60. http://dx.doi.org/10.1051/ro/2021039.

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We propose a generalized second-order asymptotic contingent epiderivative of a set-valued mapping, study its properties, as well as relations to some second-order contingent epiderivatives, and sufficient conditions for its existence. Then, using these epiderivatives, we investigate set-valued optimization problems with generalized inequality constraints. Both second-order necessary conditions and sufficient conditions for optimality of the Karush–Kuhn–Tucker type are established under the second-order constraint qualification. An application to Mond–Weir and Wolfe duality schemes is also presented. Some remarks and examples are provided to illustrate our results.

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40

Kasthuri, R., P. Vasanthi, S. Ranganayaki, and C. V. Seshaiah. "Multi-Item Fuzzy Inventory Model Involving Three Constraints: A Karush-Kuhn-Tucker Conditions Approach." American Journal of Operations Research 01, no. 03 (2011): 155–59. http://dx.doi.org/10.4236/ajor.2011.13017.

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41

Tung, Nguyen Minh. "New Higher-Order Strong Karush–Kuhn–Tucker Conditions for Proper Solutions in Nonsmooth Optimization." Journal of Optimization Theory and Applications 185, no. 2 (March 28, 2020): 448–75. http://dx.doi.org/10.1007/s10957-020-01654-5.

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42

Yadav, Naresh Kumar, Mukesh Kumar, and S. K. Gupta. "Group search optimiser-based optimal bidding strategies with no Karush–Kuhn–Tucker optimality conditions." Journal of Experimental & Theoretical Artificial Intelligence 29, no. 2 (February 9, 2016): 335–48. http://dx.doi.org/10.1080/0952813x.2015.1137694.

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43

SALMERÓN, JAVIER, and ÁNGEL MARÍN. "A CONVEX SUBMODEL WITH APPLICATION TO SYSTEM DESIGN." Asia-Pacific Journal of Operational Research 21, no. 01 (March 2004): 9–33. http://dx.doi.org/10.1142/s0217595904000047.

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In this paper, we present an algorithm to solve a particular convex model explicitly. The model may massively arise when, for example, Benders decomposition or Lagrangean relaxation-decomposition is applied to solve large design problems in facility location and capacity expansion. To attain the optimal solution of the model, we analyze its Karush–Kuhn–Tucker optimality conditions and develop a constructive algorithm that provides the optimal primal and dual solutions. This approach yields better performance than other convex optimization techniques.

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44

Zhou, Changyin, Rui Su, and Zhihui Jiang. "A Quasi-Monte-Carlo-Based Feasible Sequential System of Linear Equations Method for Stochastic Programs with Recourse." Mathematical Problems in Engineering 2017 (2017): 1–15. http://dx.doi.org/10.1155/2017/1564642.

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A two-stage stochastic quadratic programming problem with inequality constraints is considered. By quasi-Monte-Carlo-based approximations of the objective function and its first derivative, a feasible sequential system of linear equations method is proposed. A new technique to update the active constraint set is suggested. We show that the sequence generated by the proposed algorithm converges globally to a Karush-Kuhn-Tucker (KKT) point of the problem. In particular, the convergence rate is locally superlinear under some additional conditions.

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45

Flatz, Markus, and Marián Vajteršic. "Parallel Nonnegative Matrix Factorization via Newton Iteration." Parallel Processing Letters 26, no. 03 (September 2016): 1650014. http://dx.doi.org/10.1142/s0129626416500146.

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The goal of Nonnegative Matrix Factorization (NMF) is to represent a large nonnegative matrix in an approximate way as a product of two significantly smaller nonnegative matrices. This paper shows in detail how an NMF algorithm based on Newton iteration can be derived using the general Karush-Kuhn-Tucker (KKT) conditions for first-order optimality. This algorithm is suited for parallel execution on systems with shared memory and also with message passing. Both versions were implemented and tested, delivering satisfactory speedup results.

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46

Glover, B. M. "Locally compactly Lipschitzian mappings in infinite dimensional programming." Bulletin of the Australian Mathematical Society 47, no. 3 (June 1993): 395–406. http://dx.doi.org/10.1017/s0004972700015227.

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In this note we show that a subgradient multifunction of a locally compactly Lip-schitzian mapping satisfies a closure condition used extensively in optimisation theory. In addition we derive a chain rule applicable in either separable or reflexive Banach spaces for the class of locally compactly Lipschitzian mappings using a recently derived generalised Jacobian. We apply these results to the derivation of Karush-Kuhn-Tucker and Fritz John optimality conditions for general abstract cone-constrained programming problems. A discussion of constraint qualifications is undertaken in this setting.

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47

ALMEIDA, M. B., A. P. BRAGA, and J. P. BRAGA. "TRAINING SVMs WITH EDR ALGORITHM." International Journal of Neural Systems 11, no. 03 (June 2001): 257–63. http://dx.doi.org/10.1142/s0129065701000692.

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The aim of this work is to present a new training algorithm for SVMs based on the pattern selection strategy called Error Dependent Repetition (EDR). With EDR, the presentation frequency of a pattern depends on its error: patterns with larger errors are selected more frequently and patterns with smaller error (or learned) are presented with minor frequency. Using a simple iterative process based on gradient ascent, SVM-EDR can solve the dual problem without any assumption about support vectors or the Karush-Kuhn-Tucker (KKT) conditions.

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48

Antczak, Tadeusz, and Gabriel Ruiz-Garzón. "On semi-G-V-type I concepts for directionally differentiable multiobjective programming problems." An International Journal of Optimization and Control: Theories & Applications (IJOCTA) 6, no. 2 (July 29, 2016): 189–203. http://dx.doi.org/10.11121/ijocta.01.2016.00282.

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In this paper, a new class of nonconvex nonsmooth multiobjective programming problems with directionally differentiable functions is considered. The so-called G-V-type I objective and constraint functions and their generalizations are introduced for such nonsmooth vector optimization problems. Based upon these generalized invex functions, necessary and sufficient optimality conditions are established for directionally differentiable multiobjective programming problems. Thus, new Fritz John type and Karush-Kuhn-Tucker type necessary optimality conditions are proved for the considered directionally differentiable multiobjective programming problem. Further, weak, strong and converse duality theorems are also derived for Mond-Weir type vector dual programs.

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Ahmed, Huda I., Rana Z. Al-Kawaz, and Abbas Y. Al-Bayati. "Spectral Three-Term Constrained Conjugate Gradient Algorithm for Function Minimizations." Journal of Applied Mathematics 2019 (December 25, 2019): 1–6. http://dx.doi.org/10.1155/2019/6378368.

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In this work, we tend to deal within the field of the constrained optimization methods of three-term Conjugate Gradient (CG) technique which is primarily based on Dai–Liao (DL) formula. The new proposed technique satisfies the conjugacy property and the descent conditions of Karush–Kuhn–Tucker (K.K.T.). Our planned constrained technique uses the robust Wolfe line search condition with some assumptions. We tend to prove the global convergence property of the new planned technique. Numeral comparisons for (30-thirty) constrained optimization issues make sure the effectiveness of the new planned formula.

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Michelena, Nestor F., and Alice M. Agogino. "Multiobjective Hydraulic Cylinder Design." Journal of Mechanisms, Transmissions, and Automation in Design 110, no. 1 (March 1, 1988): 81–87. http://dx.doi.org/10.1115/1.3258910.

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Monotonicity analysis is used to solve a three-objective optimization problem in which a hydraulic cylinder is to be designed. With the additional application of the Karush-Kuhn-Tucker optimality conditions a reduced symbolic design chart is obtained which is then utilized to obtain parametric numerical results. Two- and three-dimensional parametric Pareto-optimal plots are obtained for the three conflicting objectives: (1) cross-sectional area, (2) circumferential stress ratio and (3) pressure ratio. The analysis and design procedure strengthens and extends the results suggested by previous works.

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