Vol. 3 No. 1 (2024): Emirati Journal of Business, Economics, & Social Studies
Articles

Mathematical Analysis of P-Stability Maps for Parametric Conic Vector Optimization

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  • Assem A. Tharwat,
  • Nahia Mourad,
  • Mohammed A. Mosilhy

Published 2024-01-16

Keywords

  • Parametric Vector Optimization Problems (PVOP),
  • Domination Cone,
  • Perturbation Maps,
  • Set-valued Maps,
  • Stability Notions

How to Cite

Mathematical Analysis of P-Stability Maps for Parametric Conic Vector Optimization. (2024). Emirati Journal of Business, Economics, & Social Studies, 3(1), 4-13. https://doi.org/10.54878/wf7f4t04

Abstract

Stability analysis for nonlinear programming systems deals with the possible changes of the system parameters and/or equations that maintain the stability of the solutions. It is a crucial requirement to study the nonlinear system and its practical values, specifically the economic impact in most real-world applications. This paper presents some outcomes in connection with stability analysis corresponding to parametric conic vector optimization problems. For these last optimization problems, two novel types of P-Stability maps, which are the P-Stability notion map and the P-Stability perturbation map, are considered based on six kinds of sets: P-feasible set, P-solvability set, the first, second, third, and fourth kinds of P-Stability notion sets with respect to a specific domination cone P. Furthermore, qualitative characteristics of the P-Stability maps under some continuity and convexity assumptions on the objective function are provided and proved. Specifically, the connections between the P-Stability maps and the P-Stability notion set are investigated. Accordingly, these characteristics were extended to the P-perturbation maps. In addition, the idea of Pstability has heavily used in different applications like network privacy, engineering fields, and some business financial models. 

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