Characterization of Unique Solvability of Absolute Value Equations: An Overview, Extensions, and Future Directions

2023/05/29 by Shubham Kumar, Kumar, Shubham, Deepmala Deepmala +3 · 1 citation
Computer Science · Mathematics · #15A18 #90C05 #90C30 #Advanced Optimization Algorithms Research #FOS: Mathematics #Matrix Theory and Algorithms #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.2305.18556

openalex publication_date 2023/05/29 · openalex created_date 2023/06/01 · openalex updated_date 2026/07/28

Abstract

This paper provides an overview of the necessary and sufficient conditions for guaranteeing the unique solvability of absolute value equations. In addition to discussing the basic form of these equations, we also address several generalizations, including generalized absolute value equations and matrix absolute value equations. Our survey encompasses known results as well as novel characterizations proposed in this study.

Cited by

• Range of optimal values in absolute value linear programming with interval data

Related

• The Unique Solvability Conditions for the Generalized Absolute Value Equations
• Sufficient conditions for the unique solvability of absolute value matrix equations
• A Note on the Paper "The unique solution of the absolute value equations"
• An Overview of Absolute Value Equations: From Theory to Solution Methods and Challenges
• Properties of the solution set of absolute value equations and the related matrix classes