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multiobjective variational problems with time delay

APPLICABLE ANALYSIS 2020年第7期99卷 1260-1269页

作者： Malinowska, Agnieszka B. Odzijewicz, Tatiana Bialystok Tech Univ Fac Comp Sci Bialystok Poland Warsaw Sch Econ Dept Math & Math Econ Warsaw Poland

In this paper, the study of multiobjective variational problems with time delay is introduced. We provide methods for identifying Pareto optimal solutions. We also prove necessary and sufficient optimality conditions ... 详细信息

关键词： Isoperimetric problems with multiple constraints time delay multiobjective variational problems Pareto optimal solutions

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η-Approximation Method for Non-convex multiobjective variational problems

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NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION 2017年第9期38卷 1125-1142页

作者： Antczak, Tadeusz Michalak, Anna Univ Lodz Fac Math & Comp Sci Lodz Poland Univ Lodz Fac Econ & Sociol Dept Econometr Rewolucji 1905 R 41 PL-90214 Lodz Poland

In this paper, we use the -approximation method for a class of non-convex multiobjective variational problems with invex functionals. In this approach, for the considered multiobjective variational problem, the associated -approximated multiobjective variational problem is constructed at the given feasible solution. The equivalence between (weakly) ecient solutions in the original multiobjective variational problem and its associated -approximated multiobjective variational problem is established under invexity hypotheses.

关键词： eta-Approximated method ecient solution invexity multiobjective variational problems

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Duality for multiobjective variational control problems with -invexity

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CALCOLO 2014年第3期51卷 393-421页

作者： Antczak, Tadeusz Univ Lodz Fac Math & Comp Sci PL-90238 Lodz Poland

In this paper, Mond-Weir and Wolfe type duals for multiobjective variational control problems are formulated. Several duality theorems are established relating efficient solutions of the primal and dual multiobjective variational control problems under -invexity. The results generalize a number of duality results previously established for multiobjective variational control problems under other generalized convexity assumptions.

关键词： multiobjective variational problems Efficient solution (Phi,rho)-invexity Duality

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On efficiency and mixed duality for a new class of nonconvex multiobjective variational control problems

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JOURNAL OF GLOBAL OPTIMIZATION 2014年第4期59卷 757-785页

作者： Antczak, Tadeusz Univ Lodz Fac Math & Comp Sci PL-90238 Lodz Poland

In this paper, we extend the notions of (Phi, rho)-invexity and generalized (Phi, rho)-invexity to the continuous case and we use these concepts to establish sufficient optimality conditions for the considered class of nonconvex multiobjective variational control problems. Further, multiobjective variational control mixed dual problem is given for the considered multiobjective variational control problem and several mixed duality results are established under (Phi, rho)-invexity.

关键词： multiobjective variational problems Efficient solution (Phi, rho)-invexity (Phi, rho)-pseudo-invexity (Phi, rho)-quasi-invexity Mixed duality

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Sufficient optimality criteria and duality for multiobjective variational control problems with -type I objective and constraint functions

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JOURNAL OF GLOBAL OPTIMIZATION 2015年第4期61卷 695-720页

作者： Antczak, Tadeusz Univ Lodz Fac Math PL-90238 Lodz Poland

In the paper, we introduce the concepts of -type I and generalized -type I functions for a new class of nonconvex multiobjective variational control problems. For such nonconvex vector optimization problems, we prove sufficient optimality conditions for weakly efficiency, efficiency and properly efficiency under assumptions that the functions constituting them are -type I and/or generalized -type I objective and constraint functions. Further, for the considered multiobjective variational control problem, its dual multiobjective variational control problem is given and several duality results are established under (generalized) -type I objective and constraint functions.

关键词： multiobjective variational problems Properly efficient solution G-type I objective and constraint functions Optimality conditions Duality

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Proper efficiency and duality for a class of multiobjective fractional variational problems containing arbitrary norms

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Optimization 1994年第4期29卷 333-347页

作者： Zalmai, G.J. Department of Mathematics and Computer Science Northern Michigan University Marquette Michigan 49855 United States

Necessary and sufficient conditions are established for properly efficient solutions of a class of nonsmooth nonconvex variational problems with multiple fractional objective functions and nonlinear inequality constraints. Based on these proper efficiency criteria, two multiobjective dual problems are constructed and appropriate duality theorems are proved. These proper efficiency and duality results also contain as special cases similar results for constrained variational problems with multiple, fractional, and conventional objective functions, which are particular cases of the main variational problem considered in this paper. © 1994, Taylor & Francis Group, LLC. All rights reserved.

关键词： arbitrary norms dual problems fractional objective functions multiobjective variational problems properly efficient solutions

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Symmetric duality for minimax multiobjective variational mixed integer programming problems with partial-invexity

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2007年第1期181卷 76-85页

作者： Chen, Xiuhong Yang, Jiangyu So Yangtze Univ Sch Informat Technol Jiangsu 214122 Peoples R China Nanjing Univ Sci & Technol Dept Comp Sci Nanjing 210094 Peoples R China

A pair of symmetric dual multiobjective variational mixed integer programs for the polars of arbitrary cones are formulated, which some primal and dual variables are constrained to belong to the set of integers. Under the separability with respect to integer variables and partial-invexity assumptions on the functions involved, we prove the weak, strong, converse and self-duality theorems to related minimax efficient solution. These results include some of available results. (c) 2006 Elsevier B.V. All rights reserved.

关键词： multiobjective variational problems mixed integer programming symmetric duality self-duality partial-invexity closed convex cone

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Duality for multiobjective fractional generalized control problems with (F, ρ)-convexity

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NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS 2004年第8期59卷 1311-1332页

作者： Park, JY Jeong, JU Dong Eui Univ Dept Math Pusan 614714 South Korea Pusan Natl Univ Dept Math Pusan 609735 South Korea

The concept of efficiency is used to formulate duality for multiobjective fractional control problems. Wolfe and Mond-Weier-type duals are formulated. Using the generalized (F, rho)-convexity on the functions involved, we establish the weak and strong duality theorems for multiobjective fractional generalized control problems. (C) 2004 Elsevier Ltd. All rights reserved.

关键词： multiobjective variational problems generalized (F, rho)-convex functions duality

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