2025 Vol.8 Dec.N06

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

  In this paper, the subdifferential of Benson proper efficiency is introduced, under suitable conditions, the existence and properties of subdifferential are proved by applying the convex set separation theorem; the stability of set-valued optimization with perturbed parameter of objective functions  are investigated in the sense of subdifferential defined under Benson proper efficiency.

  
  

• Keyword: set-valued optimization, perturbed parameter, subdifferential, stability.
• DOI: 10.12250/jpciams2025091108
• Citation form: Gongyue Wu.The Subdifferential Stability of Set-Valued Optimization With Perturbed Parameter[J]. Computer Informatization and Mechanical System,2025,Vol.8,pp.

[1] Bednarczuk E. An approach to well-posedness in vector optimization: consequences to stability. Control and Cybern, 1994(23): 107-122.

[2] X. X. Huang, Pointwise well-posedness of perturbed vector optimizations in a vector-valued variational principle, 2001, 108(3):671-686.

[3] Hou Zhenmei, Zhou Yong. The stability of set valued optimization problems under perturbed objective function. MATHEMATICA APPLICATA, 2006, 19(2): 289-295.

[4] G. Y. Chen, W. D. Rong. Characterizations of the Benson Proper efficiency for nonconvex vector optimization [J]. Journal of Optimization Theory and Applications 1998 98(2): 365-384.

[5] Xu Yihong, Liu Sanyang. Benson proper efficiency in the nearly cone-subconvexlike vector optimization with set-valued functions. Appl. Math. J. Chinese Univ. Ser. B. 2003, 18(1): 95-102.