Linear complementarity problem – Optimization Online

Global convergence and acceleration of fixed point iterations of union upper semicontinuous operators: proximal algorithms, alternating and averaged nonconvex projections, and linear complementarity problems

Published: 2022/02/21, Updated: 2022/07/19

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 propose a unified framework to analyze fixed point iterations of a set-valued operator that is the union of a finite number of upper semicontinuous maps, each with a nonempty closed domain and compact values. We discuss global convergence, local linear convergence under a calmness condition, and component identification, and further propose acceleration strategies that … 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