Mathematical Methods of Operations Research

, Volume 59, Issue 2, pp 235–247 | Cite as

A conditional gradient method with linear rate of convergence for solving convex linear systems

Abstract.

We consider the problem of finding a point in the intersection of an affine set with a compact convex set, called a convex linear system (CLS). The conditional gradient method is known to exhibit a sublinear rate of convergence. Exploiting the special structure of (CLS), we prove that the conditional gradient method applied to the equivalent minimization formulation of (CLS), converges to a solution at a linear rate, under the sole assumption that Slater’s condition holds for (CLS). The rate of convergence is measured explicitly in terms of the problem’s data and a Slater point. Application to a class of conic linear systems is discussed.

Keywords

Conic linear systems Slater’s condition conditional gradient efficiency and rate of convergence analysis 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag 2004

Authors and Affiliations

  1. 1.School of Mathematical SciencesTel-Aviv UniversityRamat-AvivIsrael

Personalised recommendations