2026 Vol.9 Feb.N01   

• Title: The Subdifferential Stability Of Set-Valued Optimization With Perturbed Order
• Name: Gongyue Wu
• Company: Science and Technolgy College of Nanchang University,Gongqingcheng,JiangXi，330031 China
• Abstract:

  This article explores the stability of set-valued optimization problems with perturbation order in constrained sets from the perspective of sub differentiation defined under Benson's true validity. The article first summarizes the basic concepts related to set-valued optimization and convex analysis, introduces key lemmas, and defines core definitions such as Benson true effective set, Benson subgradient, and subdifferential; Subsequently, a set valued optimization problem model with perturbation order was constructed, relying on spatial and mapping properties such as semi compactness, strict convexity, and semi continuity. Two core theorems were proved through lemma deduction, providing sufficient conditions for the existence of Benson sub differentiation of set valued mappings at any point with respect to perturbation order. This improved the theoretical system of stability of set valued optimization sub differentiation under perturbation order and provided new theoretical support for stability analysis of set valued optimization.

  
  

• Keyword: Set value optimization; Disturbance sequence; Benson's true effectiveness; Subdifferential stability; Convex analysis; Set-valued mapping
• DOI: 10.12250/jpciams2026090206
• Citation form: Gongyue Wu.The Subdifferential Stability Of Set-Valued Optimization With Perturbed Order [J]. Computer Informatization and Mechanical System,2026,Vol.9,pp.

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