The paper concerns new applications of advanced methods of variational analysis and generalized differentiation to constrained problems of multiobjective/vector optimization. We pay the main attention to general notions of optimal solutions for multiobjective problems that are induced by geometric concepts. of extremality in variational analysis while covering various notions of Pareto and other type of optimality/efficiency conventional in multiobjective optimization. Based on the extremal principles in variational analysis and on appropriate tools of generalized differentiation with well-developed calculus rules, we derive necessary optimality conditions for broad classes of constrained multiobjective problems in the framework of infinite-dimensional spaces. Applications of variational techniques in infinite dimensions require certain "normal compactness" properties of sets and set-valued mappings, which play a crucial rcile in deriving the main results of this paper.
Number in Series
Applied Mathematics | Mathematics
AMS Subject Classification
Primary: 49J52, 49J53; Secondary: 90C29
Mordukhovich, Boris S., "Methods of Variational Analysis in Multiobjective Optimization" (2006). Mathematics Research Reports. 36.