Well‐posedness for generalized quasi‐variational inclusion problems and for optimization problems with constraints

In this paper, well‐posedness of generalized quasi‐variational inclusion problems and of optimization problems with generalized quasi‐variational inclusion problems as constraints is introduced and studied. Some metric characterizations of well‐posedness for generalized quasi‐variational inclusion problems and for optimization problems with generalized quasi‐variational inclusion problems as constraints are given. The equivalence between the well‐posedness of generalized quasi‐variational inclusion problems and the existence of solutions of generalized quasi‐variational inclusion problems is given under suitable conditions.