Document Type
Technical Report
Abstract
The paper is devoted to new applications of advanced tools of modern variational analysis and generalized differentiation to the study of broad classes of multiobjective optimization problems subject to equilibrium constraints in both finite-dimensional and infinite-dimensional settings. Performance criteria in multiobjectivejvector optimization are defined by general preference relationships satisfying natural requirements, while equilibrium constraints are described by parameterized generalized equations/variational conditions in the sense of Robinson. Such problems are intrinsically nonsmooth and are handled in this paper via appropriate normal/coderivativejsubdifferential constructions that exhibit full calculi. Most of the results obtained are new even in finite dimensions, while the case of infinite-dimensional spaces is significantly more involved requiring in addition certain "sequential normal compactness" properties of sets and mappings that are preserved under a broad spectrum of operations.
Number in Series
2006.10
Disciplines
Applied Mathematics | Mathematics
AMS Subject Classification
90C29, 90C30, 49J52, 49J53, 49K27
Recommended Citation
Mordukhovich, Boris S., "Multiobjective Optimization Problems with Equilibrium Constraints" (2006). Mathematics Research Reports. 40.
https://digitalcommons.wayne.edu/math_reports/40
Comments
Dedicated to Steve Robinson in honor of his 65th birthday. This research was partially supported by the National Science Foundation under grants DMS-0304989 and DMS-0603846 and by the Australian Research Council under grant DP-0451168.