Article

Journal of Global Optimization

, Volume 55, Issue 1, pp 189-208

First online:

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

  • San-hua WangAffiliated withDepartment of Mathematics, Nanchang University
  • , Nan-jing HuangAffiliated withDepartment of Mathematics, Sichuan University Email author 
  • , Donal O’ReganAffiliated withDepartment of Mathematics, National University of Ireland

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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.

Keywords

Well-posedness Metric characterization Generalized quasi-variational inclusion problem Optimization problem with constraint Approximating solution sequence

Mathematics Subject Classification (2000)

49J27 49J40