# Solvers for systems of nonlinear equations and for mixed complementarity problems

## Overview of solvers for equilibrium equations

There are two types of solver for solving equilibrium equations: solvers for system of nonlinear equations and solvers for system of mixed complementarity constraints (MCP) equations. As MCP equations include as particular cases nonlinear equations, MCP solvers are perfectly able to solve also systems of traditional nonlinear equations.

For each solver, options can be defined which govern their precision, solution method or output display. There is no common pattern for these options, as RECS is only providing an interface to existing solvers, so please see solvers' documentation for how to manage options.

## MCP solvers

Four MCP solvers can be used with RECS of which three are available by default.

`lmmcp`

`lmmcp` is RECS default solver (for both MCP and traditional nonlinear problems). It is included in RECS files.

`mcpsolve`

`mcpsolve` is a faster implementation of `ncpsolve` from the CompEcon toolbox. It is a simple MCP solver that will be very fast on simple problems but that may lack robustness.

`ncpsolve`

`ncpsolve` comes with the CompEcon toolbox, which has to be installed for RECS to run.

**Path**

Path is the reference solver for mixed complementarity problems. Path has to be installed separately. It is highly recommended to install if difficult complementarity problems need to be solved. To install Path, see http://pages.cs.wisc.edu/~ferris/path.html. Path is called by the MATLAB file `recspathmcp.m`.

## Nonlinear equations solver

`fsolve`

`fsolve` is the only nonlinear equations solver interfaced with RECS. You need to have MATLAB Optimization Toolbox to use this solver.

## See also

`fsolve`, `lmmcp`, `mcpsolve`, `ncpsolve`, `recspathmcp`.