Different Conjugate Dual Problems in Vector Optimization and Their Relations

Chen, C. R.; Li, S. J.

doi:10.1007/s10957-008-9462-7

Cited by 5 publications

(2 citation statements)

References 12 publications

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“…It is known that duality assertions allow to study a minimization problem through a maximization problem and to know what one can expect in the best case. ere are many dual models in the literature, for instance, Lagrange dual (see [15,16]), Mond-Weir duality (see [17][18][19]), Wolfe duality (see [17,20]), conjugate duality (see [21]), and symmetric duality (see [22]). In this paper, we will introduce an approximate Mond-Weir dual model for the problem (VOP) and examine duality theorems between it and primal problem involving approximate quasi weakly e cient solution.…”

Section: Introductionmentioning

confidence: 99%

Optimality and Duality of Approximate Quasi Weakly Efficient Solution for Nonsmooth Vector Optimization Problems

2022

Mathematical Problems in Engineering

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This paper aims at studying optimality conditions and duality theorems of an approximate quasi weakly efficient solution for a class of nonsmooth vector optimization problems (VOP). First, a necessary optimality condition to the problem (VOP) is established by using the Clarke subdifferential. Second, the concept of approximate pseudo quasi type-I function is introduced, and under its hypothesis, a sufficient optimality condition to the problem (VOP) is also obtained. Finally, the approximate Mond–Weir dual model of the problem (VOP) is presented, and then, weak, strong, and converse duality theorems are established.

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Section: Introductionmentioning

confidence: 99%

Optimality and Duality of Approximate Quasi Weakly Efficient Solution for Nonsmooth Vector Optimization Problems

2022

Mathematical Problems in Engineering

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“…Our approach is motivated mainly by the paper [34] by Tanino. Even though Tanino [34] and related papers [31,21,4] did not mention the complete lattice structure, his results are closely related to the lattice approach. In this paper we use a classical notation which is similar to the one in [34] in order to emphasize the relationships.…”

Section: Introductionmentioning

confidence: 99%

Lagrange duality, stability and subdifferentials in vector optimization

et al. 2013

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Langrange duality theorems for vector and set optimization problems which are based on an consequent usage of infimum and supremum (in the sense greatest lower and least upper bounds with respect to a partial ordering) have been recently proven. In this note, we provide an alternative proof of strong duality for such problems via suitable stability and subdifferetial notions. In contrast to most of the related results in the literature, the space of dual variables is the same as in the scalar case, i.e., a dual variable is a vector rather than an operator. We point out that duality with operators is an easy consequence of duality with vectors as dual variables.Comment: 14 page

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