Approximate optimality conditions and sensitivity analysis in nearly convex optimization

Abstract: In this paper, approximate optimality conditions and sensitivity analysis in nearly convex optimization are discussed. More precisely, as in the spirit of convex analysis, we introduce the concept of $\varepsilon$-subdifferential for nearly convex functions. Then, we examine some significant properties and rules for the $\varepsilon$-subdifferential. These rules are applied to study optimality conditions as well as sensitivity analysis for parametric nearly convex optimization problems, which are two important topics in optimization theory.