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Quasi-monotone Subgradient Methods for Nonsmooth Convex Minimization

Author

Listed:
  • Yu. Nesterov

    (Center for Operations Research and Econometrics (CORE))

  • V. Shikhman

    (Center for Operations Research and Econometrics (CORE))

Abstract

In this paper, we develop new subgradient methods for solving nonsmooth convex optimization problems. These methods guarantee the best possible rate of convergence for the whole sequence of test points. Our methods are applicable as efficient real-time stabilization tools for potential systems with infinite horizon. Preliminary numerical experiments confirm a high efficiency of the new schemes.

Suggested Citation

  • Yu. Nesterov & V. Shikhman, 2015. "Quasi-monotone Subgradient Methods for Nonsmooth Convex Minimization," Journal of Optimization Theory and Applications, Springer, vol. 165(3), pages 917-940, June.
    • Handle: RePEc:spr:joptap:v:165:y:2015:i:3:d:10.1007_s10957-014-0677-5
    DOI: 10.1007/s10957-014-0677-5
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    Cited by:

    1. Yurii Nesterov & Vladimir Shikhman, 2017. "Distributed Price Adjustment Based on Convex Analysis," Journal of Optimization Theory and Applications, Springer, vol. 172(2), pages 594-622, February.
    2. Igor Konnov, 2020. "A Non-monotone Conjugate Subgradient Type Method for Minimization of Convex Functions," Journal of Optimization Theory and Applications, Springer, vol. 184(2), pages 534-546, February.

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