Approximate optimality conditions and sensitivity analysis in nearly convex optimization

TL;DR

This paper introduces $\

Contribution

It develops $\\varepsilon$-subdifferential concepts for nearly convex functions and applies them to optimality and sensitivity analysis in nearly convex optimization.

Findings

Established properties and rules for the $\\varepsilon$-subdifferential.

Derived approximate optimality conditions for nearly convex problems.

Performed sensitivity analysis using the new $\\varepsilon$-subdifferential framework.

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.