Approximate solutions for set optimization with an order cone that has nonempty quasirelative interiors

Abstract

In a real normed linear space, when the quasirelative interior is not empty, a class of order relation is introduced with Minkowski difference. Two classes of nonlinear functions are introduced, and their properties are discussed. A class of approximately efficient solutions and approximate weakly efficient solutions are introduced for set optimization. With nonlinear functions, optimality conditions are established for approximate solutions. Some examples are given to illustrate our main results.