Title
Sufficient conditions for global weak Pareto solutions in multiobjective optimization
Document Type
Conference Paper in Published Proceedings
Department
Mathematics and Computer Science
Publication Date
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.
http://link.springer.com/article/10.1007%2Fs11117-012-0194-4
Recommended Citation
Truong, Bao Q., and Boris Q Mordukhovich. "Sufficient conditions for global weak Pareto solutions in multiobjective optimization." Positivity 16, 3 (2012): 579-602.