For inequality constrained optimization problem, we show the existence of local saddle point of generalized augmented Lagrangian under weak second-order sufficient conditions which are weaker than the second-order sufficient conditions in the literature. We further discuss the existence of...

The augmented Lagrangian method is attractive in constraint optimizations. When it is applied to a class of constrained variational inequalities, the sub-problem in each iteration is a nonlinear complementarity problem (NCP). By introducing a logarithmic-quadratic proximal term, the sub-NCP...

In this paper, two types of Levitin–Polyak well-posedness of vector equilibrium problems with variable domination structures are investigated. Criteria and characterizations for two types of Levitin–Polyak well-posedness of vector equilibrium problems are shown. Moreover, by virtue of a gap...