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Approximate level method

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  • Richtarik, Peter

    (Université catholique de Louvain (UCL). Center for Operations Research and Econometrics (CORE))

Abstract

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.

Suggested Citation

  • Richtarik, Peter, 2008. "Approximate level method," LIDAM Discussion Papers CORE 2008083, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2008083
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    File URL: https://sites.uclouvain.be/core/publications/coredp/coredp2008.html
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    Keywords

    evel method; approximate projections in relative scale; nonsmooth convex optimization; sensitivity analysis; large-scale optimization.;
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