# American Institute of Mathematical Sciences

July  2018, 14(3): 1041-1054. doi: 10.3934/jimo.2017089

## 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

Received  February 2017 Revised  June 2017 Published  September 2017

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

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.

Citation: Liwei Zhang, Jihong Zhang, Yule Zhang. Second-order optimality conditions for cone constrained multi-objective optimization. Journal of Industrial & Management Optimization, 2018, 14 (3) : 1041-1054. doi: 10.3934/jimo.2017089
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