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Mathematical Analysis of P-Stability Maps for Parametric Conic Vector Optimization
Date
2024-02-03
Journal Title
Journal ISSN
Volume Title
Publisher
Emirates scholar
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 P
stability has heavily used in different applications like network privacy, engineering fields, and some business
financial models.
Description
Keywords
Parametric Vector Optimization Problems (PVOP); Domination Cone; Perturbation Maps; Set-valued
Maps; Stability Notions
Citation
Tharwat, A., Mourad, N. and Mosilhy, M. (2024) “Mathematical Analysis of P-Stability Maps for Parametric Conic Vector Optimization,” Emirati Journal of Business, Economics, & Social Studies, 3(1), pp. 4–13.