2025/01/11 by Morteza Rahimi, Rahimi, Morteza, Majid Soleimani-damaneh +1
Computer Science · Decision Sciences · Mathematics · #90C17 #90C29 #90C46 #Advanced Optimization Algorithms Research #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis #Risk and Portfolio Optimization
paper · pdf · doi:10.48550/arxiv.2501.06640
openalex publication_date 2025/01/11 · openalex created_date 2026/03/10 · openalex updated_date 2026/07/28
This paper delves into the challenging issues in uncertain multi-objective\noptimization, where uncertainty permeates nonsmooth nonconvex objective and\nconstraint functions. In this context, we investigate highly robust (weakly\nefficient) solutions, a solution concept defined by efficiency across all\nscenarios. Our exploration reveals important relationships between highly\nrobust solutions and other robustness notions, including set-based and\nworst-case notions, as well as connections with proper and isolated efficiency.\nLeveraging modern techniques from variational analysis, we establish necessary\nand sufficient optimality conditions for these solutions. Moreover, we explore\nthe robustness of multi-objective optimization problems in the face of various\nuncertain sets, such as ball, ellipsoidal, and polyhedral sets.\n