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

  • Amir Beck
  • Marc Teboulle


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.


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


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Copyright information

© Springer-Verlag 2004

Authors and Affiliations

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

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