Exact computation of an error bound for the balanced linear complementarity problem with unique solution

• 成果类型: Article
• 署名作者: Dussault, Jean-Pierre; Gilbert, Jean Charles
• 署名单位: University of Sherbrooke
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-022-01860-1
• 发表日期: 2023
• 页码: 1221-1238
• 关键词: optimality conditions

摘要

This paper considers the balanced form of the standard linear complementarity problem with unique solution and provides a more precise expression of an upper error bound discovered by Chen and Xiang and published in 2006. This expression has at least two advantages. It makes possible the exact computation of the error bound factor and it provides a satisfactory upper estimate of that factor in terms of the data bitlength when the data is formed of rational numbers. Along the way, we show that, when any rowwise convex combination of two square matrices is nonsingular, the l(infinity) norm of the inverse of these rowwise convex combinations is maximized by an extreme diagonal matrix.