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Smooth minimization of non-smooth functions

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  • NESTEROV, Yu.

Abstract

In this paper we propose a new approach for constructing efficient schemes for nonsmooth convex optimization. It is based on a special smoothing technique, which can be applied to the functions with explicit max-structure. Our approach can be considered as an alternative to black-box minimization. From the viewpoint of efficiency estimates, we manage to improve the traditional bounds on the number of iterations of the gradient schemes from 0 (1/e2) to 0 (1/e), keeping basically the complexity of each iteration unchanged.

Suggested Citation

  • NESTEROV, Yu., 2003. "Smooth minimization of non-smooth functions," LIDAM Discussion Papers CORE 2003012, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2003012
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    Cited by:

    1. NESTEROV, Yu, 2004. "Rounding of convex sets and efficient gradient methods for linear programming problems," LIDAM Discussion Papers CORE 2004004, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. NESTEROV, Yu, 2003. "Dual extrapolation and its applications for solving variational inequalities and related problems," LIDAM Discussion Papers CORE 2003068, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. 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).
    4. Aharon Ben-Tal & Arkadi Nemirovski, 2015. "On Solving Large-Scale Polynomial Convex Problems by Randomized First-Order Algorithms," Mathematics of Operations Research, INFORMS, vol. 40(2), pages 474-494, February.

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