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Level bundle methods for constrained convex optimization with various oracles

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  • Wim Ackooij
  • Welington Oliveira

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. Copyright Springer Science+Business Media New York 2014

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  • Wim Ackooij & Welington Oliveira, 2014. "Level bundle methods for constrained convex optimization with various oracles," Computational Optimization and Applications, Springer, vol. 57(3), pages 555-597, April.
    • Handle: RePEc:spr:coopap:v:57:y:2014:i:3:p:555-597
    DOI: 10.1007/s10589-013-9610-3
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    References listed on IDEAS

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