On Unique Solvability of the Absolute Value Equation

Authors: Jiří Rohn
Publication year: 2009
Publication type: Článek v odborném periodiku
Periodical: Optimization Letters
Projects: Development of methods for solving large scale nonlinear programming and nonsmooth optimization problems
Verification of Hybrid Systems - Exploiting the Synergy with Underlying Constraint Solving Technology
Bibliographic citation: ROHN, Jiří. On Unique Solvability of the Absolute Value Equation. Optimization Letters. 2009, 3(4), 603-606. ISSN 1862-4472. E-ISSN 1862-4480
Dostupné z: doi:10.1007/s11590-009-0129-6
DOI: 10.1007/s11590-009-0129-6
ID: 328409

Abstract

It is proved that the singular value condition $\sigma_{\max}(|B|)<\sigma_{\min}(A)$ implies unique solvability of the absolute value equation $Ax+B|x|=b$ for each right-hand side $b$.. This is a generalization of an earlier result by Mangasarian and Meyer proved for the special case of $B=-I$.