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Uncontrolled inexact information within bundle methods

  • Jérôme Malick
  • Welington de Oliveira
  • Sofia Zaourar
Original Paper

Abstract

We consider convex non-smooth optimization problems where additional information with uncontrolled accuracy is readily available. It is often the case when the objective function is itself the output of an optimization solver, as for large-scale energy optimization problems tackled by decomposition. In this paper, we study how to incorporate the uncontrolled linearizations into (proximal and level) bundle algorithms in view of generating better iterates and possibly accelerating the methods. We provide the convergence analysis of the algorithms using uncontrolled linearizations, and we present numerical illustrations showing they indeed speed up resolution of two stochastic optimization problems coming from energy optimization (two-stage linear problems and chance-constrained problems in reservoir management).

Keywords

Non-smooth optimization Bundle methods Inexact oracle Energy optimization Two-stage stochastic problems  Chance-constrained problems 

Mathematics Subject Classification

65K05 49J52 49M27 90C15 90C25 90C27 

Notes

Acknowledgments

We thank Antonio Frangioni (Univ. of Pisa, Italy) for insightful discussions on a first version of this article and Wim van Ackooij (EDF, France) for providing us with the real-life data set used in Sect. 4.2. The first author gratefully acknowledges the support of the Grant “ANR GeoLMI” and the CNRS Mastodons project “gargantua/titan”. The second author gratefully acknowledges the support provided by Severo Ochoa Program SEV-2013-0323 and Basque Government BERC Program 2014-2017.

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Copyright information

© EURO - The Association of European Operational Research Societies 2016

Authors and Affiliations

  • Jérôme Malick
    • 1
  • Welington de Oliveira
    • 2
    • 3
  • Sofia Zaourar
    • 4
    • 5
  1. 1.CNRS, LJKGrenobleFrance
  2. 2.UERJRio de JaneiroBrazil
  3. 3.BCAMBilbaoSpain
  4. 4.INRIA, UJFGrenobleFrance
  5. 5.Xerox Research Centre EuropeGrenobleFrance

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