Studniarski's derivatives and efficiency conditions for constrained vector equilibrium problems with applications

Abstract

This article is devoted to the investigation of a vector equilibrium problem involving equality, inequality and set constraints with nonsmooth functions via the higher-order Studniarski derivatives. Under the suitable constraint qualifications, higher-order Karush-Kuhn-Tucker type necessary efficiency conditions for the local weak efficient solutions of a constrained vector equilibrium problem are given. Under suitable assumptions on the objective and constraint functions, the higher-order Karush-Kuhn-Tucker type necessary optimality conditions for local weak efficient solutions become the sufficient conditions. As applications, we obtain the first-order and higher-order optimality conditions for the local weak efficient solutions of a constrained vector variational inequality problem, a constrained vector optimization problem and a transportation problem with two-sided constraints on supplies or demands in terms of Studniarski's derivatives. Several examples are also provided to illustrate the results of the paper.

Keywords:

• Higher-order necessary and sufficient efficiency conditions for constrained vector equilibrium problems
• local weak efficient solutions
• higher-order Studniarski's derivatives
• contingent cones

AMS Classifications:

• 90C46
• 91B50
• 49J52

Acknowledgments

The authors would like to express many thanks to anonymous referees for careful reading of the manuscript, which improved the paper in its present form.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The first author was supported by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grand number 101.01-2017.301.