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GENERALIZATIONS OF THE DENNIS-MOR\'E THEOREM II

Asen L. Dontchev (dontchev***at***umich.edu)

Abstract: This paper is a continuation of our previous paper were we presented generalizations of the Dennis-Mor\'e theorem to characterize q-superliner convergences of quasi-Newton methods for solving equations and variational inequalities in Banach spaces. Here we prove Dennis-Mor\'e type theorems for inexact quasi-Newton methods applied to variational inequalities in finite dimensions. We first consider variational inequalities for functions that are merely Lipschitz continuous. Then we present a parallel result for semismooth functions. An erratum to a theorem in our previous paper is also given.

Keywords: inexact quasi-Newton method, variational inequality, semismooth functions, strong metric subregularity, q-superlinear convergence

Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Category 2: Complementarity and Variational Inequalities

Category 3: Nonlinear Optimization (Constrained Nonlinear Optimization )

Citation: Mathematical Reviews, Ann Arbor, MI 48107-8604, submitted May 7, 2013

Download: [PDF]

Entry Submitted: 05/07/2013
Entry Accepted: 05/07/2013
Entry Last Modified: 05/07/2013

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