Necessary optimality conditions for countably infinite Lipschitz problems with equality constraint mappings

Abstract

The paper deals with with an optimization problem with a countably infinite system of Lipschitz equality constraints defined from an Asplund space to R. The main attention is paid to deriving new necessary optimality conditions in terms of stability conditions the constraint system. To do so, we reformulate the constraints to a generalized equation and we define a new weak constraint qualification based on the calmness property of multifunctions. © 2015, Springer-Verlag Berlin Heidelberg.