Optimality conditions for vector optimization problem governed by the cone constrained generalized equations

ABSTRACT

The paper considers a class of vector optimization problems with cone constrained generalized equations. By virtue of advanced tools of variational analysis and generalized differentiation, a limiting normal cone of the graph of the normal cone constrained by the second-order cone is obtained. Based on the calmness condition, we derive an upper estimate of the coderivative for a composite set-valued mapping. The necessary optimality condition for the problem is established under the linear independent constraint qualification. As a special case, the obtained optimality condition is simplified with the help of strict complementarity relaxation conditions. The numerical results on different examples are given to illustrate the efficiency of the optimality conditions.

KEYWORDS:

• Optimality conditions
• vector optimization
• generalized equations
• second-order cone

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 90C46
• 90C29
• 90C31
• 49J52

Acknowledgments

The authors wish to express their sincere thanks to two anonymous referees for their careful reading, helpful suggestions and comments, which improved the manuscript greatly.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The research is partially supported by Huzhou science and technology plan on No. 2016GY03 and Natural Science Foundation of China, Grant 11701061.