文章基本信息

标题：Approximate level method
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作者：Peter RICHTARIK
期刊名称：CORE Discussion Papers / Center for Operations Research and Econometrics (UCL), Louvain
出版年度：2008
卷号：1
出版社：Center for Operations Research and Econometrics (UCL), Louvain
摘要：In this paper we propose and analyze a variant of the level method [4], which is an algorithm for minimizing nonsmooth convex functions. The main work per iteration is spent on 1) minimizing a piecewise-linear model of the objective function and on 2) projecting onto the intersection of the feasible region and a polyhedron arising as a level set of the model. We show that by replacing exact computations in both cases by approximate computations, in relative scale, the theoretical iteration complexity increases only by the factor of four. This means that while spending less work on the subproblems, we are able to retain the good theoretical properties of the level method.
关键词：level method, approximate projections in relative scale, nonsmooth convex optimization, sensitivity analysis, large-scale optimization.