Weak sharp minima at infinity and solution stability in mathematical programming via asymptotic analysis

2024/10/07 by Felipe Lara, Lara, Felipe, Nguyen Van Tuyen +3 · 1 citation
Computer Science · Mathematics · #49J52 #49J53 #49K30 #49K40 #90C26 #90C31 #Advanced Optimization Algorithms Research #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.2410.04695

openalex publication_date 2024/10/07 · openalex created_date 2024/11/01 · openalex updated_date 2026/07/28

Abstract

We develop sufficient conditions for the existence of the weak sharp minima at infinity property for nonsmooth optimization problems via asymptotic cones and generalized asymptotic functions. Next, we show that these conditions are also useful for studying the solution stability of nonconvex optimization problems under linear perturbations. Finally, we provide applications for a subclass of quasiconvex functions which is stable under linear additivity and includes the convex ones.

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• Directional Subdifferentials at Infinity and Its Applications

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