Linear complementarity problem – Optimization Online

Global convergence and acceleration of projection methods for feasibility problems involving union convex sets

Published: 2022/02/21, Updated: 2023/07/14

Complementarity and Variational Inequalities, Nonlinear Optimization, Nonsmooth Optimization alternating projections, averaged projections, fixed point algorithm, global convergence, Linear complementarity problem, nonconvex optimization, proximal methods

We prove global convergence of classical projection algorithms for feasibility problems involving union convex sets, which refer to sets expressible as the union of a finite number of closed convex sets. We present a unified strategy for analyzing global convergence by means of studying fixed-point iterations of a set-valued operator that is the union of … Read more

Exact computation of an error bound for a generalized linear complementarity problem with unique solution

Published: 2021/10/20, Updated: 2021/11/20

Jean-Pierre Dussault

Jean Charles Gilbert

Complementarity and Variational Inequalities complexity, Data bitlength, error bound, Extreme diagonal matrix, Linear complementarity problem, Matrix inverse norm, p*-matrix, Rowwise convex combination of matrices, Separable function, strong duality

This paper considers a generalized 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 in 2006. This expression has at least two advantages. It makes possible the exact computation of the error bound factor and it provides a … Read more