metric regularity – Page 2 – Optimization Online

Perturbations and metric regularity

Published: 2004/12/15

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

Characterizations of error bounds for lower semicontinuous functions on metric spaces

Published: 2003/05/12, Updated: 2004/07/13

Dominique Azé

Jean-Noël Corvellec

Nonlinear Optimization, Nonsmooth Optimization error bound, metric regularity, variational methods

By using a variational method based on Ekeland’s principle, we give characterizations of the existence of so-called global and local error bounds, for lower semicontinuous functions defined on complete metric spaces. We thus provide a systematic and synthetic approach to the subject, emphasizing the special case of convex functions defined on arbitrary Banach spaces, and … Read more