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Approximate Level Method for Nonsmooth Convex Minimization

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  • Peter Richtárik

    (University of Edinburgh)

Abstract

In this paper, we propose and analyse an approximate variant of the level method of Lemaréchal, Nemirovskii and Nesterov for minimizing nonsmooth convex functions. The main per-iteration work of the level method is spent on (i) minimizing a piecewise-linear model of the objective function and (ii) projecting onto the intersection of the feasible region and a level set of the model function. We show that, by replacing exact computations in both cases by approximate computations, in relative scale, the theoretical iteration complexity increases only by a small factor which depends on the approximation level and reduces to one in the exact case.

Suggested Citation

  • Peter Richtárik, 2012. "Approximate Level Method for Nonsmooth Convex Minimization," Journal of Optimization Theory and Applications, Springer, vol. 152(2), pages 334-350, February.
    • Handle: RePEc:spr:joptap:v:152:y:2012:i:2:d:10.1007_s10957-011-9908-1
    DOI: 10.1007/s10957-011-9908-1
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    References listed on IDEAS

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    1. NESTEROV, Yu, 2003. "Unconstrained convex minimization in relative scale," LIDAM Discussion Papers CORE 2003096, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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