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An optimal subgradient algorithm for large-scale bound-constrained convex optimization

Author

Listed:
  • Masoud Ahookhosh

    (University of Vienna)

  • Arnold Neumaier

    (University of Vienna)

Abstract

This paper shows that the optimal subgradient algorithm (OSGA)—which uses first-order information to solve convex optimization problems with optimal complexity—can be used to efficiently solve arbitrary bound-constrained convex optimization problems. This is done by constructing an explicit method as well as an inexact scheme for solving the bound-constrained rational subproblem required by OSGA. This leads to an efficient implementation of OSGA on large-scale problems in applications arising from signal and image processing, machine learning and statistics. Numerical experiments demonstrate the promising performance of OSGA on such problems. A software package implementing OSGA for bound-constrained convex problems is available.

Suggested Citation

  • Masoud Ahookhosh & Arnold Neumaier, 2017. "An optimal subgradient algorithm for large-scale bound-constrained convex optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 86(1), pages 123-147, August.
    • Handle: RePEc:spr:mathme:v:86:y:2017:i:1:d:10.1007_s00186-017-0585-1
    DOI: 10.1007/s00186-017-0585-1
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    References listed on IDEAS

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    1. NESTEROV, Yu., 2005. "Smooth minimization of non-smooth functions," LIDAM Reprints CORE 1819, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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