# Nonmonotone Path Following Methods for Nonsmooth Equations and Complementarity Problems

Chapter

## Abstract

We present a homotopy path following method for nonsmooth equations, which is effective at solving highly nonlinear equations for which the norm of the residual has nonglobal local minima. The method is based on a class of homotopy mappings that are smooth in the interior of their domain. Sufficient conditions are presented that guarantee the existence of well-behaved zero curves of these homotopy mappings, which can be followed to a solution. These zero curves need not be monotonic in the homotopy parameter. The method is specialized to solve complementarity problems through the use of MCP functions and associated smoothers.

## Keywords

Nonsmooth equations complementarity problems homotopy methods smoothing path following## Preview

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