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arXiv · 2410.04710

Approximate optimality conditions and sensitivity analysis in nearly convex optimization

Nguyen Van Tuyen·Liguo Jiao·Vu Hong Quan·Duong Thi Viet An
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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.

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Nguyen Van Tuyen, Liguo Jiao, Vu Hong Quan, Duong Thi Viet An. 2024-10-07. Approximate optimality conditions and sensitivity analysis in nearly convex optimization. https://arxiv.org/abs/2410.04710

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