A first order method for finding minimal norm-like solutions of convex optimization problems

• 成果类型: Article
• 署名作者: Beck, Amir; Sabach, Shoham
• 署名单位: Technion Israel Institute of Technology; Tel Aviv University
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-013-0708-2
• 发表日期: 2014
• 页码: 25-46
• 关键词: linear-programs; regularization; perturbation

摘要

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.