Computational Optimization and Applications

, Volume 57, Issue 3, pp 555–597 | Cite as

Level bundle methods for constrained convex optimization with various oracles



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.


Nonsmooth optimization Stochastic optimization Level bundle method Chance constrained programming 



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


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© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.OSIRISEDF R&DClamartFrance
  2. 2.Ecole Centrale ParisChâtenay-MalabryFrance
  3. 3.Instituto Nacional de Matemática Pura e Aplicada—IMPARio de JaneiroBrazil

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