Jean-Pierre Dussault

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R esum e. Il est bien connu que la m ethode de Newton, lorsqu'appliqu ee a un probl eme d'in equation variationnelle fortement monotone, converge localement vers la solution de l'in equation, et que l'ordre de convergence est quadratique. Dans cet article nous mon-trons que la direction de Newton constitue une direction de descente pour un objectif non dii(More)
In this paper we propose an iterative algorithm for solving a convex quadratic program with one equality constraint and bounded variables. At each iteration, a separable convex quadratic program with the same constraint set is solved. Two variants are analyzed: one that uses an exact line search, and the other a unit step size. Preliminary testing suggests(More)
In this paper, we provide a heuristic procedure, that performs well from a global optimality point of view, for an important and difficult class of bilevel programs. The algorithm relies on an interior point approach that can be interpreted as a combination of smoothing and implicit programming techniques. Although the algorithm cannot guarantee global(More)
Abstract. We study the local behavior of a primal-dual inexact interior point methods for solving nonlinear systems arising from the solution of nonlinear optimization problems or more generally from nonlinear complementarity problems. The algorithm is based on the Newton method applied to a sequence of perturbed systems that follows by perturbation of the(More)
We present an iterative 2D tomographic reconstruction procedure for a 2D region of interest (ROI), in which high resolution is required. This method is based on an irregular sampling of the image, the ROI being defined on a fine grid while the rest of the image--the "background"--is sampled on a much coarser grid. The background and the ROI are(More)
We consider the inversion of a linear operator with centered Gaussian white noise by MAP estimation with a Gaussian prior distribution on the solution. The actual estimator is computed approximately by a numerical method. We propose a relation between the stationarity measure of this approximate solution to the mean square error of the exact solution. This(More)