The CoMirror algorithm for solving nonsmooth constrained convex problems

Authors:
Amir Beck;Aharon Ben-Tal;Nili Guttmann-Beck;Luba Tetruashvili
Affiliations:
Faculty of Industrial Engineering and Management, Technion - Israel Institute of Technology, Israel;Faculty of Industrial Engineering and Management, Technion - Israel Institute of Technology, Israel;Department of Computer Science, The Academic College of Tel-Aviv Yafo, Yafo, Israel;Faculty of Industrial Engineering and Management, Technion - Israel Institute of Technology, Israel
Venue:
Operations Research Letters
Year:
2010

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Abstract

We introduce a first-order Mirror-Descent (MD) type algorithm for solving nondifferentiable convex problems having a combination of simple constraint set X (ball, simplex, etc.) and an additional functional constraint. The method is tuned to exploit the structure of X by employing an appropriate non-Euclidean distance-like function. Convergence results and efficiency estimates are derived. The performance of the algorithm is demonstrated by solving certain image deblurring problems.