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Excessive gap technique in non-smooth convex minimization

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  • NESTEROV, Yurii

Abstract

In this paper we introduce a new primal-dual technique for convergence analysis of gradient schemes for non-smooth convex optimization. As an example of its application, we derive a primal-dual gradient method for a special class of structured non-smooth optimization problems, which ensures a rate of convergence of the order O(1/k), where k is the iteration count. Another example is a gradient scheme which minimizes a non-smooth strongly convex function with known structure with the rate of convergence O(1/k exp2). In both cases the effciency of the methods is higher than the corresponding black-box lower complexity bounds by an order of magnitude.

Suggested Citation

  • NESTEROV, Yurii, 2003. "Excessive gap technique in non-smooth convex minimization," LIDAM Discussion Papers CORE 2003035, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2003035
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    Cited by:

    1. NESTEROV, Yurii, 2004. "Smoothing technique and its applications in semidefinite optimization," LIDAM Discussion Papers CORE 2004073, 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).

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