Near Convexity and Generalized Differentiation

2023/02/17 by Nam, Nguyen Mau, Thieu, Nguyen Nang, Yen, Nguyen Dong · 1 citation
#49J52 #49J53 #90C31 #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2302.08986

Abstract

In this paper, we introduce the concept of nearly convex set-valued mappings and investigate fundamental properties of these mappings. Additionally, we establish a geometric approach for generalized differentiation of nearly convex set-valued mappings and nearly convex functions. Our contributions expand the current knowledge of nearly convex sets and functions, while providing several new results pertaining to nearly convex set-valued mappings.

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• Qualitative and Generalized Differentiation Properties of Optimal Value Functions with Applications to Duality

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