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

Amir Beck () and Marc Teboulle ()

Mathematical Methods of Operations Research, 2004, vol. 59, issue 2, 235-247

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. Copyright Springer-Verlag 2004

Keywords: Conic linear systems; Slater’s condition; conditional gradient; efficiency and rate of convergence analysis (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1007/s001860300327

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