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Optimality conditions and duality for mathematical programming with equilibrium constraints including multiple interval-valued objective functions on Hadamard manifolds

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JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS 2024年第2期41卷 1105-1136页

作者： Tung, L. T. Singh, V. Can Tho Univ Coll Nat Sci Dept Math Can Tho 900000 Vietnam Natl Inst Technol Mizoram Dept Math Aizawl 796012 Mizoram India

This paper investigates mathematical programming with equilibrium constraints including multiple interval-valued objective functions on Hadamard manifolds. In the first part, both necessary and sufficient optimality conditions for some types of efficient solutions are considered. After that, the Wolfe and Mond-Weir type dual problems are formulated and the duality relations under geodesic convexity assumptions are examined. Some examples are proposed to illustrate the results.

关键词： Multiobjective mathematical programming Equilibrium constraints interval-valued objective functions Hadamard manifolds Karush-Kuhn-Tucker optimality conditions Mond-Weir and Wolfe duality

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Karush-Kuhn-Tucker optimality conditions and duality for convex semi-infinite programming with multiple interval-valued objective functions

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JOURNAL OF APPLIED MATHEMATICS AND COMPUTING 2020年第1-2期62卷 67-91页

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

This paper deals with convex semi-infinite programming with multiple interval-valued objective functions. We first investigate necessary and sufficient Karush-Kuhn-Tucker optimality conditions for some types of optimal solutions. Then, we formulate types of Mond-Weir and Wolfe dual problems and explore duality relations under convexity assumptions. Some examples are provided to illustrate the advantages of our results in some cases.

关键词： Multiobjective convex semi-infinite programming interval-valued objective functions Karush-Kuhn-Tucker optimality conditions Mond-Weir duality Wolfe duality

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KARUSH-KUHN-TUCKER OPTIMALITY CONDITIONS AND DUALITY FOR A SEMI-INFINITE PROGRAMMING WITH MULTIPLE interval-valued objective functions

JOURNAL OF NONLINEAR FUNCTIONAL ANALYSIS

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JOURNAL OF NONLINEAR FUNCTIONAL ANALYSIS 2019年 2019卷

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

This paper deals with a semi-infinite programming with multiple interval-valued objective functions. We first investigate necessary and sufficient Karush-Kuhn-Tucker optimality conditions for some types of optimal solutions. Then, we formulate types of Mond-Weir and Wolfe dual problems and explore duality relations under convexity assumptions. Some examples are provided to illustrate our results.

关键词： Multiobjective semi-infinite programming interval-valued objective functions Karush-Kuhn-Tucker optimality conditions Mond-Weir duality Wolfe duality

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Second-order necessary and sufficient optimality conditions for multiobjective interval-valued nonlinear programming

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APPLICABLE ANALYSIS 2025年第4期104卷 691-718页

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

In this article, the second-order optimality conditions for nonlinear programming with multiple interval-valued objective functions (in brief, NPMIOF) are studied. In the first part, the second- and first-order necessary optimality conditions for some types of efficient solutions of NPMIOF are established under of Abadie second- and first-order constraint qualifications. In the next part, we investigate both primal and dual second-order sufficient optimality conditions. Our second-order necessary conditions enhance the previous results. The second-order sufficient optimality conditions are new.

关键词： Multiobjective nonlinear programming interval-valued objective functions second-order necessary and sufficient optimality conditions second-order Abadie constraint qualifications

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