## NMHP Matlab function

`NMHP` is a Matlab function that solves the linear
complementarity problem in standard form.
### Description of the function

`NMHP` solves the linear complementarity problem in the form
$0 \leq x \perp (Mx+q) \geq 0$,

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.

### Authors

Jean-Pierre Dussault

Département d'Informatique, Faculté des Sciences, Université de Sherbrooke, Québec, Canada

Jean-Pierre.Dussault@Usherbrooke.ca

ORCID 0000-0001-7253-7462
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

### Documentation

There is no other documentation than the one inside the function, which
is accessible by entering
`help nmhp`

in a `Matlab` window.
### Associated publication

You are invited to read and cite the following paper, on which the code
is grounded:
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]

### Version

Version 1.1 (April 2019).
### License

The function is distributed under the QPL license.
### Upload

The code has been uploaded on Software Heritage on 10-07-2023, via HAL.
### Download

`nmhp-1.1`