A Modified Levenberg-Marquardt Method for Nonsmooth Equations with Finitely Many Maximum Functions

Abstract EN

For solving nonsmooth systems of equations, the Levenberg-Marquardt method and its variants are of particular importance because of their locally fast convergent rates.

Finitely many maximum functions systems are very useful in the study of nonlinear complementarity problems, variational inequality problems, Karush-Kuhn-Tucker systems of nonlinear programming problems, and many problems in mechanics and engineering.

In this paper, we present a modified Levenberg-Marquardt method for nonsmooth equations with finitely many maximum functions.

Under mild assumptions, the present method is shown to be convergent Q-linearly.

Some numerical results comparing the proposed method with classical reformulations indicate that the modified Levenberg-Marquardt algorithm works quite well in practice.