On the Nonemptiness and Boundedness of Solution Sets of Weakly Homogeneous Optimization Problems

2020/01/26 by Vu Trung Hieu, Hieu, Vu Trung · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Packing Problems #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.2001.09436

openalex publication_date 2020/01/26 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

In this paper, we introduce a new class of optimization problems whose objective functions are weakly homogeneous relative to the constraint sets. By using the normalization argument in asymptotic analysis, we prove two criteria for the nonemptiness and boundedness of the solution set of a weakly homogeneous optimization problem. Moreover, the normalization argument enables us to study the existence and stability of the solution sets of linearly parametric optimization problems. Several examples are given to illustrate the derived results.

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