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Level Bundle Methods for Constrained Convex Optimization with Various Oracles

Wim van Ackooij (wim.van-ackooij***at***edf.fr)
Welington de Oliveira (wlo***at***impa.br)

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 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.

Keywords: Nonsmooth Optimization · Stochastic Optimization · Level Bundle Method · Chance Constrained Programming

Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

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Entry Submitted: 05/23/2013
Entry Accepted: 05/23/2013
Entry Last Modified: 08/29/2013

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