$0 \leq x \perp (Mx+q) \geq 0$,where $M$ is a real matrix of order $n$ and $q$ is a real vector of length $n$. In plain words, the problem consists in searching a vector $x$ such that the components of $x$ and $Mx+q$ are nonnegative and $x^\mathsf{T}(Mx+q) = 0$.
NMHP solves the problem by the Newton-min algorithm with the Harker and Pang globalization technique.
Mathieu Frappier
Département de Mathématiques, Faculté des Sciences, Université de Sherbrooke, Québec, Canada
Mathieu.Frappier@usherbrooke.ca
Jean Charles Gilbert
INRIA (centre de recherche Inria de Paris), 2 rue Simone Iff, CS 42112, 75589 Paris Cedex 12, France
Département de Mathématiques, Faculté des Sciences, Université de Sherbrooke, Québec, Canada
Jean-Charles.Gilbert@inria.fr
ORCID 0000-0002-0375-4663
help nmhpin a Matlab window.
A lower bound on the iterative complexity of the Harker and Pang globalization technique of the Newton-min algorithm for solving the linear complementarity problem, by J.-P. Dussault, M. Frappier and J.Ch. Gilbert, EURO Journal on Computational Optimization, 7:4 (2019) 359-380. [doi]