Second-order optimality conditions for cone constrained multi-objective optimization

Liwei Zhang; Jihong Zhang; Yule Zhang

doi:10.3934/jimo.2017089

Article Contents

2018, Volume 14, Issue 3: 1041-1054. Doi: 10.3934/jimo.2017089

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Second-order optimality conditions for cone constrained multi-objective optimization

School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China

* Corresponding authorr: Liwei Zhang
* Corresponding authorr: Liwei Zhang

Received: February 2017

Revised: June 2017

Early access: August 2017

Published: June 2018

Supported by the National Natural Science Foundation of China under project grant No. 11571059,11731013 and No. 91330206.

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Abstract

The aim of this paper is to develop second-order necessary and second-order sufficient optimality conditions for cone constrained multi-objective optimization. First of all, we derive, for an abstract constrained multi-objective optimization problem, two basic necessary optimality theorems for weak efficient solutions and a second-order sufficient optimality theorem for efficient solutions. Secondly, basing on the optimality results for the abstract problem, we demonstrate, for cone constrained multi-objective optimization problems, the first-order and second-order necessary optimality conditions under Robinson constraint qualification as well as the second-order sufficient optimality conditions under upper second-order regularity for the conic constraint. Finally, using the optimality conditions for cone constrained multi-objective optimization obtained, we establish optimality conditions for polyhedral cone, second-order cone and semi-definite cone constrained multi-objective optimization problems.

Keywords:

Cone constrained multi-objective optimization,
second-order optimality conditions,
polyhedral cone,
second-order cone,
semi-definite cone.

Mathematics Subject Classification: Primary: 90C29, 90C46.

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