Optimality conditions for approximate solutions in multiobjective optimization problems

Ying Gao; Xinmin Yang; Heung Wing Joseph Lee

doi:10.1155/2010/620928

Optimality conditions for approximate solutions in multiobjective optimization problems

Ying Gao
, Xinmin Yang
, Heung Wing Joseph Lee

Research output: Journal article publication › Journal article › Academic research › peer-review

8 Citations (Scopus)

Abstract

We study first- and second-order necessary and sufficient optimality conditions for approximate (weakly, properly) efficient solutions of multiobjective optimization problems. Here, tangent cone, -normal cone, cones of feasible directions, second-order tangent set, asymptotic second-order cone, and Hadamard upper (lower) directional derivatives are used in the characterizations. The results are first presented in convex cases and then generalized to nonconvex cases by employing local concepts.

Original language	English
Article number	620928
Journal	Journal of Inequalities and Applications
Volume	2010
DOIs	https://doi.org/10.1155/2010/620928
Publication status	Published - 1 Dec 2010

ASJC Scopus subject areas

Analysis
Applied Mathematics
Discrete Mathematics and Combinatorics

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10.1155/2010/620928

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abstract = "We study first- and second-order necessary and sufficient optimality conditions for approximate (weakly, properly) efficient solutions of multiobjective optimization problems. Here, tangent cone, -normal cone, cones of feasible directions, second-order tangent set, asymptotic second-order cone, and Hadamard upper (lower) directional derivatives are used in the characterizations. The results are first presented in convex cases and then generalized to nonconvex cases by employing local concepts.",

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AU - Gao, Ying

AU - Yang, Xinmin

AU - Lee, Heung Wing Joseph

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N2 - We study first- and second-order necessary and sufficient optimality conditions for approximate (weakly, properly) efficient solutions of multiobjective optimization problems. Here, tangent cone, -normal cone, cones of feasible directions, second-order tangent set, asymptotic second-order cone, and Hadamard upper (lower) directional derivatives are used in the characterizations. The results are first presented in convex cases and then generalized to nonconvex cases by employing local concepts.

AB - We study first- and second-order necessary and sufficient optimality conditions for approximate (weakly, properly) efficient solutions of multiobjective optimization problems. Here, tangent cone, -normal cone, cones of feasible directions, second-order tangent set, asymptotic second-order cone, and Hadamard upper (lower) directional derivatives are used in the characterizations. The results are first presented in convex cases and then generalized to nonconvex cases by employing local concepts.

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U2 - 10.1155/2010/620928

DO - 10.1155/2010/620928

M3 - Journal article

SN - 1025-5834

VL - 2010

JO - Journal of Inequalities and Applications

JF - Journal of Inequalities and Applications

M1 - 620928

ER -

Optimality conditions for approximate solutions in multiobjective optimization problems

Abstract

ASJC Scopus subject areas

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