Set-valued equilibrium problems based on the concept of null set with applications

On Sub Convexlike Optimization Problems

“…Our Lagrangian theorems (Theorems 6 and 7) are generalizations of Lagrangian theorems in [14] and modifications of those in [10,15]. We can also extended the results in [12] according to our methods used in this paper.…”

“…The mathematical programs with equilibrium constraints are a class of optimization problem with variational inequality constraints. By representing the variational inequality as a generalized equation, e.g., [10][11][12], a mathematical program with equilibrium constraints can be reformulated as an optimization problem with an equality constraint. This paper works with a set-valued optimization problem with inequality, equality as well as abstract constraints.…”