Quasi-monotone subgradient methods for nonsmooth convex minimization

Nesterov, Yurii;Shikhman, Vladimir
(2015) Journal of Optimization Theory and Applications — Vol. 165, n° 3, p. 917-940 (2015)

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Authors
  • Nesterov, YuriiUCLouvain
    Author
  • Shikhman, VladimirUCLouvain
    Author
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.
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Nesterov, Y., & Shikhman, V. (2015). Quasi-monotone subgradient methods for nonsmooth convex minimization. Journal of Optimization Theory and Applications, 165(3), 917-940. https://doi.org/10.1007/s10957-014-0677-5 (Original work published 2015)