Level bundle methods for constrained convex optimization with various oracles

Wim Ackooij () and Welington Oliveira ()

Computational Optimization and Applications, 2014, vol. 57, issue 3, 555-597

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

Keywords: Nonsmooth optimization; Stochastic optimization; Level bundle method; Chance constrained programming (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (26)

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DOI: 10.1007/s10589-013-9610-3

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