On the optimality conditions for D.C. vector optimization problems

Abstract

In this paper, by using the notions of approximate pseudo-dissipativity, strong subdifferential and epsilon-subdifferential, we present sufficient optimality conditions for an epsilon-weak local Pareto minimal solution and an epsilon-local Pareto minimal solution of a vector optimization problem, where its objective function and constraint set are in the form of differences of two vector-valued convex maps, respectively. Then, an application of the given result is obtained for vector fractional programming. Also, some comments are given on two recently published papers presented by Guo and Li [Optimality conditions for vector optimization problems with difference of convex maps. J Optim Theory Appl. 2014;162:821–844] and Gadhi and Metrane [Sufficient optimality condition for vector optimization problems under D.C. J Glob Optim. 2004;28:55–66].

Keywords:

• Convex mapping
• optimality conditions
• local weak minimal solution
• subdifferential
• minimal point

Acknowledgments

The authors are grateful to Professor Christiane Tammer for her valuable and constructive remarks.

Disclosure statement

No potential conflict of interest was reported by the author(s).