On second-order Karush--Kuhn--Tucker optimality conditions for C^1,1 vector optimization problems

2025/03/02 by Nguyễn Văn Tuyên, Van Tuyen, Nguyen
Computer Science · Mathematics · #49J52 #49J53 #49K30 #90C29 #90C46 #Differential Equations and Numerical Methods #FOS: Mathematics #Nonlinear Differential Equations Analysis #Optimization and Control (math.OC) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.2503.00927

openalex publication_date 2025/03/02 · openalex created_date 2025/10/12 · openalex updated_date 2026/07/28

Abstract

This paper focuses on optimality conditions for C^1,1 vector optimization problems with inequality constraints. By employing the limiting second-order subdifferential and the second-order tangent set, we introduce a new type of second-order constraint qualification in the sense of Abadie. Then we establish some second-order necessary optimality conditions of Karush--Kuhn--Tucker-type for local (weak) efficient solutions of the considered problem. In addition, we provide some sufficient conditions for a local efficient solution of the such problem. The obtained results improve existing ones in the literature.

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