Levitin-Polyak Well-Posedness for Generalized Quasi-Variational Inclusion and Disclusion Problems and Optimization Problems With Constraints

Abstract

In this paper, Levitin-Polyak well-posedness for generalized quasivariational inclusion and disclusion problems are introduced and studied. Necessary and sufficient conditions for Levitin-Polyak well-posedness of these problems are proved. Moreover, Levitin-Polyak well-posedness for optimization problems with generalized quasi-variational inclusion problems, generalized quasi-variational disclusion problems and scalar generalized quasi-equilibrium problems as constraints are also given under some suitable conditions.

Levitin-polyakwell-posedness for set-valued optimization problems with constraints

“…Lin and Chuang [18] investigated the well-posedness in the generalized sense for variational inclusion problems and variational disclusion problems, the wellposedness for optimization problems with variational inclusion problems, variational disclusion problems and scalar equilibrium problems as constraints. In 2012, Wang and Huang [22] studied the necessary and sufficient conditions for the Levitin-Polyak well-posedness of generalized quasi-variational inclusion and disclusion problems and for optimization problems with constraints in Hausdorff topological vector spaces. In many practical problems, their constraints appear in the form of systems.…”