Level bundle methods for constrained convex optimization with various oracles |
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Authors: | Wim van Ackooij Welington de Oliveira |
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Affiliation: | 1. OSIRIS, EDF R&D, 1 avenue du Général de Gaulle, 92141, Clamart, France 2. Ecole Centrale Paris, Grande Voie des Vignes, 92295, Chatenay-Malabry, France 3. Instituto Nacional de Matemática Pura e Aplicada—IMPA, Rua Dona Castorina 110, 22460-320, Rio de Janeiro, Brazil
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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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