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

Authors:
San-Hua Wang;Nan-Jing Huang;Donal O'Regan
Affiliations:
Department of Mathematics, Nanchang University, Nanchang, People's Republic of China 330031;Department of Mathematics, Sichuan University, Chengdu, People's Republic of China 610064;Department of Mathematics, National University of Ireland, Galway, Ireland
Venue:
Journal of Global Optimization
Year:
2013

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Abstract

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.