Inexact Newton methods for variational inequalities

Abstract

We study convergence of inexact Newton methods for solving variational inequalities. First, we consider an extension of the method proposed by Dembo, Eisenstat, and Steihaug for solving equations. We show how regularity properties of the the mapping involved in the variational inequality are able to guarantee that every sequence generated by the method is convergent either linearly, superlinearly, or quadratically, according to the particular assumptions. Then we consider a class of quasi-Newton methods for variational inequalities for which we give a generalization of the Dennis-MorTeX Embedding failed! theorem.

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