A first order method for finding minimal norm-like solutions of convex optimization problems |
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Authors: | Amir Beck Shoham Sabach |
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Institution: | 1. Faculty of Industrial Engineering and Management, Technion-Israel Institute of Technology, 32000?, Haifa, Israel 2. School of Mathematical Sciences, Tel-Aviv University, 69978?, Ramat-Aviv, Israel
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Abstract: | We consider a general class of convex optimization problems in which one seeks to minimize a strongly convex function over a closed and convex set which is by itself an optimal set of another convex problem. We introduce a gradient-based method, called the minimal norm gradient method, for solving this class of problems, and establish the convergence of the sequence generated by the algorithm as well as a rate of convergence of the sequence of function values. The paper ends with several illustrating numerical examples. |
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