Faculty Works

Title

Sufficient conditions for global weak Pareto solutions in multiobjective optimization

Document Type

Conference Paper in Published Proceedings

Department

Mathematics and Computer Science

2012

Abstract

In this paper we derive new sufficient conditions for global weak Pareto solutions to set-valued optimization problems with general geometric constraints of the type $$\mbox{\rm maximize}\quad F(x) \quad \mbox{subject to}\quad x\in \O,$$ \noindent where $F: X \tto Z$ is a set-valued mapping between Banach spaces with a partial order on $Z$. Our main results are established by using advanced tools of variational analysis and generalized differentiation; in particular, the extremal principle and full generalized differential calculus for the subdifferential/coderivative constructions involved. Various consequences and refined versions are also considered for special classes of problems in vector optimization including those with Lipschitzian data, with convex data, with finitely many objectives, and with no constraints.