arXiv subjects

Ta Quang Son

Publications and source records attributed to Ta Quang Son.

2 recordsLinked to original sources

arXiv2019

Optimality conditions for approximate Pareto solutions of a nonsmooth vector optimization problem with an infinite number of constraints

In this paper, we present some new necessary and sufficient optimality conditions in terms of the Clarke subdifferentials for approximate Pareto solutions of a nonsmooth vector optimization problem which has an infinite number of constraints. As a consequence, we obtain optimality conditions for the particular cases of cone-constrained convex vector optimization problems and semidefinite vector optimization problems. Examples are given to illustrate the obtained results.

math.OC↗

arXiv2019

On AKKT optimality conditions for cone-constrained vector optimization problems

In this paper, we introduce a kind of approximate Karush--Kuhn--Tucker condition (AKKT) for a smooth cone-constrained vector optimization problem. We show that, without any constraint qualification, the AKKT condition is a necessary for a local weak efficient solution of the considered problem. For convex problems, we prove that the AKKT condition is a necessary and sufficient optimality condition for a global weak efficient solution. We also introduce some strict constraint qualifications associated with the AKKT condition.

math.OC↗