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Second-order duality for nondifferentiable multiobjective programming problems

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION 2007年第9-10期28卷 975-988页

作者： Ahmad, I. Sharma, Sarita Aligarh Muslim Univ Dept Math Aligarh 202002 Uttar Pradesh India

This paper is concerned with second-order duality for a class of nondifferentiable multiobjective programming problems. Usual duality theorems are proved for Mangasarian type and general Mond-Weir type vector duals un... 详细信息

关键词： generalized bonvexity nondifferentiable multiobjective programming properly efficient solution second-order duality

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Unified higher order duality in nondifferentiable multiobjective programming involving cones

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MATHEMATICAL AND COMPUTER MODELLING 2012年第3-4期55卷 419-425页

作者： Ahmad, Izhar King Fahd Univ Petr & Minerals Dept Math & Stat Dhahran 31261 Saudi Arabia

In this paper, a unified higher order dual is formulated for a nondifferentiable multiobjective programming problem, where every component of the objective function contains a term involving the support function of a compact convex set. Results about duality are presented under more suitable conditions. This higher order symmetric dual formulation unifies the symmetric dual formulations in the literature. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： nondifferentiable multiobjective programming Higher order duality Efficient solutions Support function Cones Higher order generalized type-I functions

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Optimality conditions and duality for nondifferentiable multiobjective programming problems involving d-r-type I functions

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2009年第1期225卷 236-250页

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

In this paper, new classes of nondifferentiable functions constituting multiobjective programming problems are introduced. Namely, the classes of d-r-type I objective and constraint functions and, moreover, the various classes of generalized d-r-type I objective and constraint functions are defined for directionally differentiable multiobjective programming problems. Sufficient optimality conditions and various Mond-Weir duality results are proved for nondifferentiable multiobjective programming problems involving functions of such type. Finally, it is showed that the introduced d-r-type I notion with r not equal 0 is not a sufficient condition for Wolfe weak duality to hold. These results are illustrated in the paper by suitable examples. (C) 2009 Published by Elsevier B.V.

关键词： nondifferentiable multiobjective programming (weak) Pareto optimal solution d-r-type I objective and constraint functions Optimality conditions Duality

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Second order duality for nondifferentiable multiobjective programming problem involving (F, α, ρ, d)-V-type I functions

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OPTIMIZATION LETTERS 2010年第2期4卷 211-226页

作者： Jayswal, Anurag Kumar, Dilip Kumar, Rajnish Birla Inst Technol Extens Ctr Dept Appl Math Patna 800014 Bihar India Birla Inst Technol Dept Appl Math Ranchi 835215 Jharkhand India

In this paper, new classes of second order (F, alpha, rho, d)-V-type I functions for a nondifferentiable multiobjective programming problem are introduced. Furthermore, second order Mangasarian type and general Mond-Weir type duals problems are formulated for a nondifferentiable multiobjective programming problem. Weak strong and strict converse duality theorems are studied in both cases assuming the involved functions to be second order (F, alpha, rho, d)-V-type I.

关键词： nondifferentiable multiobjective programming Efficiency Generalized convexity Second order duality Type I functions

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Generalized second order symmetric duality in nondifferentiable multiobjective programming

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TAIWANESE JOURNAL OF MATHEMATICS 2007年第3期11卷 745-764页

作者： Kim, Do Sang Lee, Hyo Jung Lee, Yu Jung Pukyong Natl Univ Dept Appl Math Pusan 608737 South Korea

We introduce a pair of multiobjective generalized second order symmetric dual programs where the objective function contains a support function. Weak, strong and converse duality theorems for these second order problems are established under suitable generalized second order convexity assumptions. Also, we give some special cases of our second order symmetric duality results.

关键词： nondifferentiable multiobjective programming Generalized convex functions Second order symmetric duality

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Second order symmetric duality for nondifferentiable multiobjective programming involving cones

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TAIWANESE JOURNAL OF MATHEMATICS 2008年第6期12卷 1347-1363页

作者： Kim, Do Sang Kang, Hun Suk Lee, Yu Jung Pukyong Natl Univ Dept Appl Math Pusan 608737 South Korea

We construct Mond-Weir and Wolfe types of nondifferentiable multiobjective second order symmetric dual problems with cone constraints over arbitrary closed convex cones. Weak, strong, and converse duality theorems for weakly efficient solutions are established under the assumptions of second order invex and pseudo-invex functions. Several known results are obtained as special cases of our symmetric duality.

关键词： nondifferentiable multiobjective programming second order generalized convexity functions second order symmetric duality

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nondifferentiable higher order duality in multiobjective programming involving cones

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NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS 2009年第12期71卷 E2474-E2480页

作者： Kin, Do Sang Lee, Yu Jung Pukyong Natl Univ Div Math Sci Pusan South Korea

We introduce the nondifferentiable multiobjective problem involving cone constraints, where every component of the objective function contains a term involving the support function of a compact convex set. For this problem, Wolfe and Mond-Weir type duals are proposed. We establish weak, strong duality theorems for an efficient solution under suitable higher order generalized invexity conditions. As special cases of our duality relations, we give some known duality results. (C) 2009 Elsevier Ltd. All rights reserved.

关键词： nondifferentiable multiobjective programming Higher order duality Support function Higher order generalized invexity

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nondifferentiable multiobjective symmetric duality with F-convexity over cones

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NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS 2011年第5期74卷 1577-1584页

作者： Saini, Himani Gulati, T. R. Indian Inst Technol Roorkee Dept Math Roorkee 247667 Uttar Pradesh India

In the present paper, a pair of Wolfe type nondifferentiable multiobjective second-order symmetric dual programs over arbitrary cones are formulated. Using the concept of weak efficiency with respect to a convex cone, weak, strong and converse duality theorems are studied under second-order K-F-convexity assumptions. Self-duality is also discussed. (C) 2010 Elsevier Ltd. All rights reserved.

关键词： nondifferentiable multiobjective programming Symmetric duality Second-order K-F-convexity Cone constraints Weakly efficient solution Duality theorems

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nondifferentiable multiobjective SECOND ORDER SYMMETRIC DUALITY WITH CONE CONSTRAINTS

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TAIWANESE JOURNAL OF MATHEMATICS 2008年第8期12卷 1943-1964页

作者： Kim, Do Sang Lee, Yu Jung Lee, Hyo Jung Pukyong Natl Univ Dept Appl Math Pusan 608737 South Korea

We introduce two pairs of nondifferentiable multiobjective second order symmetric dual problems with cone constraints over arbitrary closed convex cones, which is different from the one proposed by Mishra and Lai [12]. Under suitable second order pseudo-invexity assumptions we establish weak, strong and converse duality theorems as well as self-duality relations. Our symmetric duality results include an extension of the symmetric duality results for the first order case obtained by Kim and Kim [7] to the second order case. Several known results are abtained as special cases.

关键词： nondifferentiable multiobjective programming Generalized convex functions Second order symmetric duality

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nondifferentiable multiobjective Wolfe Type Symmetric Duality under Invexity

Nondifferentiable Multiobjective Wolfe Type Symmetric Dualit...

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International Conference on Soft Computing for Problem Solving (SocProS 2011)

作者： Gulati, T. R. Verma, Khushboo Indian Inst Technol Roorkee Dept Math Roorkee 247667 Uttar Pradesh India

In the present paper, a pair of Wolfe type nondifferentiable mutiobjective second-order programm involving two kernel function is formulated. We prove Weak, Strong and Converse duality theorem for the second-order sym... 详细信息

ISBN: (纸本)9788132204862

关键词： nondifferentiable multiobjective programming Second-order symmetric duality Proper efficiency Invexity

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