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