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Level bundle methods for constrained convex optimization with various oracles

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Abstract

We propose restricted memory level bundle methods for minimizing constrained convex nonsmooth optimization problems whose objective and constraint functions are known through oracles (black-boxes) that might provide inexact information. Our approach is general and covers many instances of inexact oracles, such as upper, lower and on-demand accuracy oracles. We show that the proposed level bundle methods are convergent as long as the memory is restricted to at least four well chosen linearizations: two linearizations for the objective function, and two linearizations for the constraints. The proposed methods are particularly suitable for both joint chance-constrained problems and two-stage stochastic programs with risk measure constraints. The approach is assessed on realistic joint constrained energy problems, arising when dealing with robust cascaded-reservoir management.

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Acknowledgements

The authors are grateful to the reviewer for his suggestions of improvement.

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Authors and Affiliations

  1. OSIRIS, EDF R&D, 1 avenue du Général de Gaulle, 92141, Clamart, France

    Wim van Ackooij

  2. Ecole Centrale Paris, Grande Voie des Vignes, 92295, Châtenay-Malabry, France

    Wim van Ackooij

  3. Instituto Nacional de Matemática Pura e Aplicada—IMPA, Rua Dona Castorina 110, 22460-320, Rio de Janeiro, Brazil

    Welington de Oliveira

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  1. Wim van Ackooij
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  2. Welington de Oliveira
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Correspondence to Wim van Ackooij.

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van Ackooij, W., de Oliveira, W. Level bundle methods for constrained convex optimization with various oracles. Comput Optim Appl 57, 555–597 (2014). https://doi.org/10.1007/s10589-013-9610-3

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