Publications (10)0 Total impact
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ABSTRACT: Image recovery problems can be solved using optimization techniques. In this case, they often lead to the resolution of either a large scale quadratic program, or, equivalently, to a nondifferentiable minimization problem. Interior point methods are widely known for their efficiency in linear programming. Lately, they have been extended with success to the resolution of linear complementary problems, (LCP), which include convex quadratic programming. We present an infeasible predictor-corrector interior point method, in the general framework of monotone (LCP). The algorithm has polynomial complexity. We also prove it converges globally, with asymptotic quadratic rate. We apply this method to the alenoising of images. In the implementation we take advantage of the underlying structure of the problem, specially its sparsky. We obtain good performances, that we assess by comparing the method with a variable-metric proximal bundle algorithm applied to the resolution of the equivalent nonsmooth problem.
08/1997;
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ABSTRACT: : In this work we study the optimization of a production system comprising a multi-item single machine with piecewise deterministic demands. Demands can only take a finite number of values and the demand changes are described by Poisson processes. We present the theoretical characterization of the solution and a numerical procedure to solve it. We establish the rate of convergence of the discrete solution toward the original continuous solution. Key-words: scheduling problems, piecewise deterministic demands, quasi-variational inequalities, Hamilton-Jacobi-Bellman equation, numerical solution (R'esum'e : tsvp) CONICET -- Inst. Beppo Levi, Dpto. Matem'atica, Fac. Cs. Ex., Ing. y Agr., Universidad Nacional de Rosario, Rosario, Argentine. This paper is included in the activities developed in the frame of the Cooperation Projet INRIA--Instituto de Matem'atica Bepp 3 o Levi, Coordinators of the projet: E. Rofman--R. Gonz'alez Unite de recherche INRIA Rocquencourt Domaine de Voluceau, Roc...
04/1997;
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ABSTRACT: : We consider a set of problems which consists of systems of coupled variational inequalities. To solve these problems we use a decomposition--coordination method which allows us to solve the coupled problem through the solution of simple independent problems -- in general, they are linear problems or simple obstacle problems. In this approach, the original problem is stated in terms of some appropriately defined auxiliary variables. These variables are modified (by an iterative algorithm in the coordination phase of the procedure) until the desired global solution is obtained. . Key-words: junction problems, variational inequalities, decomposition methods, convex function, unilateral condition, bilateral condition, numerical solution, iterative algorithm (R'esum'e : tsvp) CONICET -- Inst. Beppo Levi, Dpto. Matem'atica, Fac. Cs. Ex., Ing. y Agr., Universidad Nacional de Rosario, Rosario, Argentine. This paper is included in the activities developed in the frame of the Cooperation Pr...
04/1997;
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ABSTRACT: : We study the control of conservative discrete time dynamical systems when there are incomplete information and finite memory controllers. We state results for the asymptotic stability in the case of finite dimension and in the case of infinite dimension, we give an example where it is impossible to get asymptotic stability. Key-words: Asymptotic stability, conservative systems, control without regret, incomplete information, finite memory controllers, discrete time systems. (R'esum'e : tsvp) CONICET -- Inst. Beppo Levi, Dpto. Matem'atica, Fac. Cs. Ex., Ing. y Agr., Universidad Nacional de Rosario, Rosario, Argentine. This paper is included in the activities developed in the frame of the Cooperation Projet INRIA--Instituto de Matem'atica Beppo Levi, Coordinators of the projet: E. Rofman--R. Gonz'alez Unit de recherche INRIA Rocquencourt Domaine de Voluceau, Rocquencourt, BP 105, 78153 LE CHESNAY Cedex (France) Tlphone : (33 1) 39 63 55 11 -- Tlcopie : (33 1) 39 63 53 30 Controle ...
04/1997;
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ABSTRACT: : A minimax optimal control problem with infinite horizon is considered. Some properties of the optimal cost function u are studied. Among them, the issue of regularity and the characterization of u in terms of the associated Hamilton-JacobiBellman (HJB) equation. Relations between subsolutions and supersolutions of the HJB equation are also analyzed. Key-words: minimax optimal control problem, infinite horizon, worst case, subsolutions, supersolutions, Hamilton-Jacobi-Bellman equation. (R'esum'e : tsvp) CONICET -- Inst. Beppo Levi, Dpto. Matem'atica, Fac. Cs. Ex., Ing. y Agr., Universidad Nacional de Rosario, Rosario, Argentine. This paper is included in the activities developed in the frame of the Cooperation Projet INRIA--Instituto de Matem'atica Beppo Levi, Coordinators of the projet: E. Rofman--R. Gonz'alez Unite de recherche INRIA Rocquencourt Domaine de Voluceau, Rocquencourt, BP 105, 78153 LE CHESNAY Cedex (France) Telephone : (33 1) 39 63 55 11 -- Telecopie : (33 1) 39 63...
10/1996;
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ABSTRACT: : We consider here a stochastic discrete minimax optimal control problem defined on a finite state Markov chain in the case of infinite horizon. We prove the existence of an optimal control in terms of a generalized feedback policies. We characterize the optimal cost function and we present iterative methods to compute it numerically. Key-words: stochastic control, optimal control, minimax optimization, Markov chain, value iteration, policy iteration, feedback. (R'esum'e : tsvp) CONICET -- Inst. Beppo Levi, Dpto. Matem'atica, Fac. Cs. Ex., Ing. y Agr., Universidad Nacional de Rosario, Rosario, Argentine. This paper is included in the activities developed in the frame of the Cooperation Projet INRIA--Instituto de Matem'atica Beppo Levi, Coordinators of the projet: E. Rofman--R. Gonz'alez Unite de recherche INRIA Rocquencourt Domaine de Voluceau, Rocquencourt, BP 105, 78153 LE CHESNAY Cedex (France) Telephone : (33 1) 39 63 55 11 -- Telecopie : (33 1) 39 63 53 30 Un probl`eme de co...
10/1996;
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ABSTRACT: An algorithm for minimizing a nonlinear function subject to nonlinear equality and inequality constraints is described. It can be seen as an extension of primal interior point methods to non-convex optimization. The new algorithm applies sequential quadratic programming techniques to a sequence of barrier problems, and uses trust regions to ensure the robustness of the iteration and to allow the direct use of second order derivatives. An analysis of the convergence properties of the new method is presented.
07/1996;
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ABSTRACT: : Optimizing the daily production in an electrical network (the socalled unit-commitment problem) is an heterogeneous large-scale problem (some 200 power plants in the French network). It lends itself particularly well to Lagrangian decomposition, which results in a nonsmooth optimization problem. The present report concerns the application of a bundle method to this problem, following various decomposition schemes. This work was the object of a contract between the French Electricity Board (EdF) and Inria. Key-words: unit-commitment problem, optimization, Lagrangian relaxation, bundle method (R'esum'e : tsvp) Rapport Final - Contrat EdF n ffi R31/1J3669/ER238 -- octobre 1995 Unite de recherche INRIA Rocquencourt Domaine de Voluceau, Rocquencourt, BP 105, 78153 LE CHESNAY Cedex (France) Telephone : (33 1) 39 63 55 11 -- Telecopie : (33 1) 39 63 53 30 Application de la m'ethode de faisceaux `a la gestion journali`ere de la production R'esum'e : L'optimisation de la production...
03/1996;
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ABSTRACT: : To minimize a convex function f , we state a class of penalty-type bundle algorithms, where the penalty uses a variable metric. This metric is updated according to quasi-Newton formulae based on Moreau-Yosida approximations of f . In particular, we introduce a "reversal" quasi-Newton formula, specially suited for our purpose. We consider several variants in the algorithm and discuss their respective merits. Furthermore, we accept a degenerate penalty term in the regularization. Key-words: Bundle methods, convex optimization, mathematical programming, proximal point, quasi-Newton algorithms, variable metric. (R'esum'e : tsvp) Unite de recherche INRIA Rocquencourt Domaine de Voluceau, Rocquencourt, BP 105, 78153 LE CHESNAY Cedex (France) Telephone : (33 1) 39 63 55 11 -- Telecopie : (33 1) 39 63 53 30 Une classe de m'ethodes de faisceaux `a m'etrique variable R'esum'e : Pour minimiser une fonction convexe f , nous proposons une classe d'algorithmes de type faisceaux avec p'enalit...
09/1994;
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ABSTRACT: : When computing the infimal convolution of a convex function f with the squared norm, one obtains the so-called Moreau-Yosida regularization of f . Among other things, this function has a Lipschitzian gradient. We investigate some more of its properties, relevant for optimization. Our main result concerns second-order differentiability and is as follows. Under assumptions that are quite reasonable in optimization, the Moreau-Yosida is twice diffferentiable if and only if f is twice differentiable as well. In the course of our development, we give some results of general interest in convex analysis. In particular, we establish primaldual relationship between the remainder terms in the first-order development of a convex function and its conjugate. Key-words: Convex optimization, mathematical programming, proximal point, secondorder differentiability. (R'esum'e : tsvp) Unite de recherche INRIA Rocquencourt Domaine de Voluceau, Rocquencourt, BP 105, 78153 LE CHESNAY Cedex (France) Telep...
09/1994;
