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Mathematical Analysis of P-Stability Maps for Parametric Conic Vector Optimization
Date
2024
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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.