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- Warren Hare, Claudia A. Sagastizábal
- SIAM Journal on Optimization
- 2010

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)

- Claude Lemaréchal, Claudia A. Sagastizábal
- SIAM Journal on Optimization
- 1997

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)

At a given point p, a convex function f is differentiable in a certain subspace U (the subspace along which ∂f(p) has 0-breadth). This property opens the way to defining a suitably restricted second derivative of f at p. We do this via an intermediate function, convex on U . We call this function the U-Lagrangian; it coincides with the ordinary Lagrangian… (More)

- Léonard Bacaud, Claude Lemaréchal, Arnaud Renaud, Claudia A. Sagastizábal
- Comp. Opt. and Appl.
- 2001

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)

- Laura Bahiense, Nelson Maculan, Claudia A. Sagastizábal
- Math. Program.
- 2002

- Robert Mifflin, Claudia A. Sagastizábal
- Math. Program.
- 2005

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)

- Welington de Oliveira, Claudia A. Sagastizábal
- Optimization Methods and Software
- 2014

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)

For a convex function, we consider a space decomposition that allows us to identify a subspace on which a Lagrangian related to the function appears to be smooth. We study a particular trajectory, that we call a fast track, on which a certain second-order expansion of the function can be obtained. We show how to obtain such fast tracks for a general class… (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)

- Welington Luis de Oliveira, Claudia A. Sagastizábal, Susana Scheimberg
- SIAM Journal on Optimization
- 2011

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)