Error bounds and a condition number for the absolute value equations

• 成果类型: Article
• 署名作者: Zamani, Moslem; Hladik, Milan
• 署名单位: Tilburg University; Charles University Prague
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-021-01756-6
• 发表日期: 2023
• 页码: 85-113
• 关键词: smooth newton method; weak sharp minima; convergence analysis; Infinity norm; COMPLEMENTARITY; inverse; algorithms

摘要

Due to their relation to the linear complementarity problem, absolute value equations have been intensively studied recently. In this paper, we present error bound conditions for absolute value equations. Along with the error bounds, we introduce a condition number. We consider general scaled matrix p-norms, as well as particular p-norms. We discuss basic properties of the condition number, including its computational complexity. We present various bounds on the condition number, and we give exact formulae for special classes of matrices. Moreover, we consider matrices that appear based on the transformation from the linear complementarity problem. Finally, we apply the error bound to convergence analysis of two methods for solving absolute value equations.