Claudia A. Sagastizábal

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Proximal bundle methods have been shown to be highly successful optimization methods for unconstrained convex problems with discontinuous first derivatives. This naturally leads to the question of whether proximal variants of bundle methods can be extended to a nonconvex setting. This work proposes an approach based on generating cutting-planes models, not(More)
When computing the infimal convolution of a convex function f with the squared norm, the so-called Moreau–Yosida regularization of f is obtained. Among other things, this function has a Lipschitzian gradient. We investigate some more of its properties, relevant for optimization. The most important part of our study concerns second-order differentiability:(More)
A specialized variant of bundle methods suitable for large-scale problems with separable objective is presented. The method is applied to the resolution of a stochastic unit-commitment problem solved by Lagrangian relaxation. The model includes hydroas well as thermal-powered plants. Uncertainties lie in the demand, which evolves in time according to a tree(More)
For convex minimization we introduce an algorithm based on VU-space decomposition. The method uses a bundle subroutine to generate a sequence of approximate proximal points. When a primal-dual track leading to a solution and zero subgradient pair exists, these points approximate the primal track points and give the algorithm’s V, or corrector, steps. The(More)
For nonsmooth convex optimization, we consider level bundle methods built using an oracle that computes values for the objective function and a subgradient at any given feasible point. For the problems of interest, the exact oracle information is computable, but difficult to obtain. In order to save computational effort the oracle can provide estimations(More)
We consider the inclusion of commitment of thermal generation units in the optimal management of the Brazilian power system. By means of Lagrangian relaxation we decompose the problem and obtain a nondifferentiable dual function that is separable. We solve the dual problem with a bundle method. Our purpose is twofold: first, bundle methods are the methods(More)
Stochastic programming problems arise in many practical situations. In general, the deterministic equivalents of these problems can be very large and may not be solvable directly by general-purpose optimization approaches. For the particular case of two-stage stochastic programs, we consider decomposition approaches akin to a regularized L-shaped method(More)