Solving convex programs by random walks

In breakthrough developments about two decades ago, L. G. Khachiyan [14] showed that the Ellipsoid method solves linear programs in polynomial time, while M. Grötschel, L. Lovász and A. Schrijver [4, 5] extended this to the problem of minimizing a convex function over any convex set specified by a separation oracle. In 1996, P. M. Vaidya [21] improved the running time via a more sophisticated algorithm. We present a simple new algorithm for convex optimization based on sampling by a random walk; it also solves for a natural generalization of the problem.

Authors

• Dimitris Bertsimas
• Santosh S. Vempala

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