Optimality criteria and duality in multiple-objective optimization involving generalized invexity

Kaul, R. N.; Suneja, Surjeet Kaur; Srivastava, M. P.

doi:10.1007/bf02207775

Cited by 113 publications

(56 citation statements)

References 6 publications

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“…x f x Following Jeyakumar and Mond [24], Kaul et al [8] and Slimani and Radjef [20], we give the following definitions. , : , :…”

Section: Preliminaries and Definitionsmentioning

confidence: 99%

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Efficiency and Duality in Nondifferentiable Multiobjective Programming Involving Directional Derivative

Ismail¹

2011

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In this paper, we introduce a new class of generalized d I -univexity in which each component of the objective and constraint functions is directionally differentiable in its own direction d i for a nondifferentiable multiobjective programming problem. Based upon these generalized functions, sufficient optimality conditions are established for a feasible point to be efficient and properly efficient under the generalised d I -univexity requirements. Moreover, weak, strong and strict converse duality theorems are also derived for Mond-Weir type dual programs.

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“…x f x Following Jeyakumar and Mond [24], Kaul et al [8] and Slimani and Radjef [20], we give the following definitions. , : , :…”

Section: Preliminaries and Definitionsmentioning

confidence: 99%

“…Kaul et al [8] extended the concept of type I and its generalizations for a multiobjective programming problem. They investigated optimality conditions and derived Wolfe type and Mond-Weir type duality results.…”

Section: Introductionmentioning

confidence: 99%

Efficiency and Duality in Nondifferentiable Multiobjective Programming Involving Directional Derivative

Ismail¹

2011

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“…The concept of type-I functions was first introduced by Hanson and Mond [1] as a generalization of convexity. With and without differentiability, the type-I functions were extended to several classes of generalized type-I functions by many researchers, and sufficient optimality criteria and duality results are established for multi-objective programming (vector optimization) problems involving these functions (see [1][2][3][4][5][6][7][8][9][10][11][12]). Another meaningful generalization of convex functions is the introduction of arcwise connected functions, which was given by Avriel and Zang [13].…”

Section: Introductionmentioning

confidence: 99%

Optimality for Multi-Objective Programming Involving Arcwise Connected d-Type-I Functions

Yu¹,

Wang²

2011

AJOR

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This paper deals with the optimality conditions and dual theory of multi-objective programming problems involving generalized convexity. New classes of generalized type-I functions are introduced for arcwise connected functions, and examples are given to show the existence of these functions. By utilizing the new concepts, several sufficient optimality conditions and Mond-Weir type duality results are proposed for non-differentiable multi-objective programming problem.

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“…Later, Hanson and Mond 3 defined two new classes of functions, called type I and type II functions, which have been further generalized by many researchers and applied to nonlinear programming problems in different settings. This concept was further generalized 2 Journal of Inequalities and Applications to pseudo-type I and quasi-type I functions by Rueda and Hanson 4 and to pseudoquasi-type I, quasi-pseudo-type I, and strictly quasi-pseudo-type I functions by Kaul et al 5 .…”

Section: Introductionmentioning

confidence: 99%

Optimality and Duality in Nonsmooth Multiobjective Optimization Involving V-Type I Invex Functions

et al. 2010

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A new class of generalized V-type I invex functions is introduced for nonsmooth multiobjective programming problem. Based upon these generalized invex functions, we establish sufficient optimality conditions for a feasible point to be an efficient or a weakly efficient solution. Weak, strong, and strict converse duality theorems are proved for Mond-Weir type dual program in order to relate the weakly efficient solutions of primal and dual programs.

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Optimality criteria and duality in multiple-objective optimization involving generalized invexity

Cited by 113 publications

References 6 publications

Efficiency and Duality in Nondifferentiable Multiobjective Programming Involving Directional Derivative

Efficiency and Duality in Nondifferentiable Multiobjective Programming Involving Directional Derivative

Optimality for Multi-Objective Programming Involving Arcwise Connected d-Type-I Functions

Optimality and Duality in Nonsmooth Multiobjective Optimization Involving V-Type I Invex Functions

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