Relative Pareto minimizers for multiobjective problems: existence and optimality conditions |
| |
Authors: | Truong Q Bao Boris S Mordukhovich |
| |
Institution: | 1. Department of Mathematics, Wayne State University, Detroit, MI, 48202, USA
|
| |
Abstract: | In this paper we introduce and study enhanced notions of relative Pareto minimizers for constrained multiobjective problems
that are defined via several kinds of relative interiors of ordering cones and occupy intermediate positions between the classical
notions of Pareto and weak Pareto efficiency/minimality. Using advanced tools of variational analysis and generalized differentiation,
we establish the existence of relative Pareto minimizers for general multiobjective problems under a refined version of the
subdifferential Palais-Smale condition for set-valued mappings with values in partially ordered spaces and then derive necessary
optimality conditions for these minimizers (as well as for conventional efficient and weak efficient counterparts) that are
new in both finite-dimensional and infinite-dimensional settings. Our proofs are based on variational and extremal principles
of variational analysis; in particular, on new versions of the Ekeland variational principle and the subdifferential variational
principle for set-valued and single-valued mappings in infinite-dimensional spaces. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|