Optimality conditions for vector optimization problems with variable ordering structures

Author: Eichfelder Gabriele  

Publisher: Taylor & Francis Ltd

ISSN: 0233-1934

Source: Optimization, Vol.62, Iss.5, 2013-05, pp. : 597-627

Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.

Previous Menu Next

Abstract

Our main concern in this article are concepts of nondominatedness w.r.t. a variable ordering structure introduced by Yu [P.L. Yu, Cone convexity, cone extreme points, and nondominated solutions in decision problems with multiobjectives, J. Optim. Theory Appl. 14 (1974), pp. 319-377]. Our studies are motivated by some recent applications e.g. in medical image registration. Restricting ourselves to the case when the values of a cone-valued map defining the ordering structure are Bishop-Phelps cones, we obtain for the first time scalarizing functionals for nondominated elements, Fermat rule, Lagrange multiplier rule and duality results for a single- or set-valued vector optimization problem with a variable ordering structure.