Asen L. Dontchev – Optimization Online

GENERALIZATIONS OF THE DENNIS-MOR\’E THEOREM II

Published: 2013/05/07

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 … Read more

Perturbations and metric regularity

Published: 2004/12/15

Asen L. Dontchev

Adrian Lewis

Nonsmooth Optimization condition number, distance to ill-posedness, eckart-young theorem, metric regularity, regularity modulus, riemannian manifold, set-valued mapping

A point x is an approximate solution of a generalized equation [b lies in F(x)] if the distance from the point b to the set F(x) is small. Metric regularity of the set-valued mapping F means that, locally, a constant multiple of this distance bounds the distance from x to an exact solution. The smallest … Read more