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STRONG KARUSH-KUHN-TUCKER OPTIMALITY CONDITIONS FOR multiobjective semi-infinite programming VIA TANGENTIAL SUBDIFFERENTIAL

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RAIRO-OPERATIONS RESEARCH 2018年第4-5期52卷 1019-1041页

作者： Le Thanh Tung Can Tho Univ Dept Math Coll Nat Sci Can Tho 900000 Vietnam

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.

关键词： multiobjective semi-infinite programming efficient solution weakly efficient solution strong Karush-Kuhn-Tucker optimality conditions tangential subdifferential

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Lagrange Duality and Saddle Point Optimality Conditions for multiobjective semi-infinite programming with Vanishing Constraints

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NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION 2024年第1期45卷 44-81页

作者： Tung, Le Thanh Tam, Dang Hoang Khai, Tran Thien Can Tho Univ Coll Nat Sci Dept Math Can Tho Vietnam Univ Sci Fac Math & Comp Sci Ho Chi Minh City Vietnam Vietnam Natl Univ Ho Chi Minh City Vietnam Tra Vinh Univ Ctr Training & Enterprise Cooperat Tra Vinh Vietnam

The objective of this paper is to investigate multiobjective semi-infinite programming problems with vanishing constraints (in brief, MSIPVC). We firstly propose both the vector Lagrange dual problems and the scalarized Lagrange dual problems for MSIPVC and explore duality relations under convexity assumptions. Then, the saddle point optimality conditions for MSIPVC are considered. Some examples are also given to illuminate the main results.

关键词： multiobjective semi-infinite programming saddle point optimality conditions scalarized Lagrange dual problems vanishing constraints vector Lagrange dual problems

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Optimality conditions for nonsmooth interval-valued and multiobjective semi-infinite programming (vol 55, pg 13, 2021)

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RAIRO-OPERATIONS RESEARCH 2021年第1期55卷 23-25页

作者： Jennane, Mohsine Kalmoun, El Mostafa Lafhim, Lahoussine Sidi Mohamed Ben Abdellah Univ Dept Math FSDM Fes Morocco Qatar Univ Dept Math Stat & Phys Doha Qatar

This note corrects an error in our paper [RAIRO: OR 55 (2021) 1-11] as we should drop the expression "with at least one strict inequality" in the definition of interval order in Section 2. Instead of proposing this short amendment, the authors of [RAIRO: OR 55 (2021) 13-22] gave a proposition that requires an additional condition on the constraint functions. However, we claim that all the results of our paper are correct once the modification above is done.

关键词： multiobjective semi-infinite programming interval-valued functions optimality conditions

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Strong Karush-Kuhn-Tucker Optimality Conditions for Borwein Properly Efficient Solutions of multiobjective semi-infinite programming

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BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY 2021年第1期52卷 1-22页

作者： Le Thanh Tung Can Tho Univ Coll Nat Sci Dept Math Can Tho 900000 Vietnam

In this paper, we study strong Karush-Kuhn-Tucker optimality conditions for Borwein properly efficient solutions of multiobjective semi-infinite programming. By using some regularity conditions in the sense of Mordukhovich subdifferentials and Clarke subdifferentials, we obtain some strong necessary optimality conditions for Borwein properly efficient solutions. Some examples are also provided to illustrate that our regularity conditions have more advantages than the previous regularity conditions in some cases.

关键词： multiobjective semi-infinite programming Mordukhovich subdifferentials Clarke subdifferentials Borwein properly efficient solutions Strong KKT optimality conditions

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Optimality Conditions and Duality for multiobjective semi-infinite programming on Hadamard Manifolds

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BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY 2022年第5期48卷 2191-2219页

作者： Le Thanh Tung Dang Hoang Tam Can Tho Univ Coll Nat Sci Dept Math Can Tho 900000 Vietnam

This article is devoted to studying the problem of multiobjective semi-infinite programming on Hadamard manifolds. We first establish both Karush-Kuhn-Tucker necessary and sufficient optimality conditions for some type of efficient solutions. Then, we propose Wolfe and Mond-Weir-type dual problems and examine duality relations under geodesic convexity assumptions.

关键词： multiobjective semi-infinite programming Karush-Kuhn-Tucker optimality conditions Mond-Weir duality Wolfe duality Hadamard manifolds Geodesic convexity

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Duality and Saddle Point for multiobjective semi-infinite programming

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JOURNAL OF INTERDISCIPLINARY MATHEMATICS 2014年第1期17卷 27-39页

作者： Dang, Linli An, Gang Xian Shiyou Univ Coll Sci Xian 710065 Peoples R China

This paper is devoted to study the mixed dual models for a class of non-smooth multiobjective semi-infinite programming problems in which the index set of the inequality constraints is an arbitrary set not necessarily finite. Weak duality conclusions are derived and proved for mixed type multiobjective dual programs, using the generalized uniform convexity on the functions involved. Some previous duality results for differentiable semi-infinite programming problems turn out to be special cases for the results described in the paper. Furthermore, the vector saddle point theory is discussed for the semi-infinite programming problems. The results extend and improve the corresponding results in the literature.

关键词： Generalized uniform K - (F,alpha,rho,d) - convexity multiobjective semi-infinite programming duality saddle point

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Karush-Kuhn-Tucker optimality conditions and duality for multiobjective semi-infinite programming with vanishing constraints

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ANNALS OF OPERATIONS RESEARCH 2022年第2期311卷 1307-1334页

作者： Tung, Le Thanh Can Tho Univ Dept Math Coll Nat Sci Can Tho 900000 Vietnam

This paper concentrates on studying multiobjective semi-infinite programming with vanishing constraints. Firstly, the necessary and sufficient Karush-Kuhn-Tucker optimality conditions for multiobjective semi-infinite programming with vanishing constraints are considered. Then, we formulate Wolfe and Mond-Weir type dual problems and establish duality relations under convexity assumptions. Some examples are proposed to verify our results.

关键词： multiobjective semi-infinite programming Vanishing constraints Constraint qualifications Karush-Kuhn-Tucker optimality conditions Mond-Weir duality Wolfe duality

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Duality for multiobjective semi-infinite programming with Uniform K - (F_b, ρ)-convexity

Duality for Multiobjective Semi-infinite Programming with Un...

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9th International Conference on Computational Intelligence and Security (CIS)

作者： Yang, Hong Yulin Coll Sch Math & Stat Yulin Peoples R China

ISBN: (纸本)9781479925483

In this paper, new classes of generalized convex functions called uniform K - (F-b, rho)- convex, uniform K - (F-b, rho)- pseudoconvex, uniform K - (F-b, rho)- quasiconvex functions are defined using K-directional derivative and K-subdifferential. multiobjective semi-infinite programming involving these generalized convex functions is researched, some Mond-Weir type duality results are obtained.

关键词： K - (F-b, rho)- convex function uniform K - (F-b, rho)- pseudoconvex function uniform K - (F-b, rho)- quasiconvex function multiobjective semi-infinite programming Mond-Weir type duality

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STRONG KARUSH-KUHN-TUCKER OPTIMALITY CONDITIONS AND DUALITY FOR NONSMOOTH multiobjective semi-infinite programming VIA MICHEL-PENOT SUBDIFFERENTIAL

JOURNAL OF NONLINEAR FUNCTIONAL ANALYSIS

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JOURNAL OF NONLINEAR FUNCTIONAL ANALYSIS 2017年 2017卷

作者： Le Thanh Tung Can Tho Univ Coll Nat Sci Dept Math Can Tho Vietnam

The aim of this paper is to study strong Karush-Kuhn-Tucker optimality conditions and duality for nonsmooth multiobjective semi-infinite programming. By using the Michel-Penot subdifferential and suitable generalized regularity conditions, we establish the strong necessary and sufficient optimality conditions for some kind of efficient solutions of nonsmooth multiobjective semi-infinite programming. We also propose Wolfe and Mond-Weir duality schemes for multiobjective semi-infinite programming and explore weak and strong duality relations under the generalized convexity.

关键词： multiobjective semi-infinite programming KKT optimality condition Wolfe duality Mond-Weir duality Michel-Penot subdifferential

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Optimality Conditions for a class of Nondifferentiable multiobjective semi-infinite programming

Optimality Conditions for a class of Nondifferentiable Multi...

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2012 International Conference on Computer Science and Mathematics,Physical Education and Management（ICCMPE 2012）

作者： Rongbo Wang Yan’an University College of Mathematics and Computer science Yan’an China Qiang Feng Yan’an University College of Mathematics and Computer science Yan’an China

A class of new symmetric differentiable generalized uniform B -（p,r）- Invexity function are given by using symmetric gradient. The optimality conditions for a class of nondifferentiable multiobjective semi-infinite programming are obtained under this new generalized invexity functions. The work generalized many results on programming problems with invex functions, B- Invexity functions, （p,r）-Invexity functions,and B-（p,r）- Invexity function.

关键词： multiobjective semi-infinite programming symm -etric differentiable generalized uniform B -（p,r）-Invexity function efficient solutions

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