Uncontrolled inexact information within bundle methods

Jérôme Malick 1, * Welington de Oliveira 2 Sofia Zaourar-Michel 3
* Corresponding author
1 DAO - Données, Apprentissage et Optimisation
LJK - Laboratoire Jean Kuntzmann
3 BIPOP - Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
Abstract : We consider convex nonsmooth optimization problems where additional information with uncontrolled accuracy is readily available. It is often the case when the objective function is itself the output of an optimization solver, as for large-scale energy optimization problems tackled by decomposition. In this paper, we study how to incorporate the uncontrolled linearizations into (proximal and level) bundle algorithms in view of generating better iterates and possibly accelerating the methods. We provide the convergence analysis of the algorithms using uncontrolled linearizations, and we present numerical illustrations showing they indeed speed up resolution of two stochastic optimization problems coming from energy optimization (two-stage linear problems and chance-constrained problems in reservoir management).
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Jérôme Malick, Welington de Oliveira, Sofia Zaourar-Michel. Uncontrolled inexact information within bundle methods. EURO Journal on Computational Optimization, Springer, 2017, 5 (1), pp.5-29. ⟨10.1007/s13675-015-0060-9⟩. ⟨hal-01249261⟩



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