Subdifferential necessary conditions for extremal solutions to set-valued optimization problems with equilibrium constraints

Document Type

Conference Paper in Published Proceedings


Mathematics and Computer Science

Publication Date



This paper concerns new subdifferential necessary conditions for local optimal solutions to an important class of general set-valued optimization problems with abstract equilibrium constraints, where the optimality notion is understood in the sense of the generalized order from Definition~5.53 in the book ``Variational Analysis and Generalized Differentiation II: Applications" by B. Mordukhovich. This notion is induced by the concept of set extremality and covers all the conventional notions of optimality in vector optimization. Our method is mainly based on advanced tools of variational analysis and generalized differentiation. Our results are formulated in terms of the subdifferential constructions for set-valued mappings. We also provide several important relationships between subdifferentials and coderivatives of set-valued mappings including formulas, sequentially normal compactness property, and Lipschitz-like behavior which are new in vector optimization and even in scalar optimization.