# Nonlinear Complementarity Problems (NCP)¶

The problem:

Find $$z \in \mathcal{R}^n_+$$ such that:

$\begin{equation*} 0 \le z \perp F(z) \ge 0 \end{equation*}$

Available solvers/formulations::

Problem Statement:

Given a sufficiently smooth function $${F}\colon {{\mathrm{I\!R}}}^{n} \to {{\mathrm{I\!R}}}^{n}$$ The Nonlinear Complementarity Problem (NCP) is to find two vectors $$(z,w \in {{\mathrm{I\!R}}}^{n})$$ such that:

\begin{split}\begin{align*} w &= F(z) \\ 0 &\le w \perp z \ge 0 \end{align*}\end{split}

Available solvers::

• ncp_FBLSA(), nonsmooth Newton method based on Fisher-Burmeister function with a line search.
• ncp_pathsearch() , a solver based on a path search method