Séance WA11 - Optimisation multi-niveaux / Multilevel Optimization
Jour mercredi, le 06 mai 2009 Salle Demers Beaulne Président Melodie Mouffe
Présentations
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10h30- 10h55 |
Multilevel Trust-Region Method in Infinity-Norm for Bound-Constrained Optimization |
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Serge Gratton, CERFACS, Parallel Algorithms Team, 42, Avenue G. Coriolis, Toulouse Cedex, France, 31057 Melodie Mouffe, CERFACS, Parallel Algorithms Team, 42, Avenue G. Coriolis, Toulouse Cedex, France, 31057 Philippe L. Toint, Université de Namur, Département de Mathématique, Rempart de la Vierge 8, Namur, Belgique, 5000 Recently, people have tried to apply the ideas of multigrid methods in the optimization framework, in the case where the objective function arises from the discretization of an underlying continuous function. Coarser discretizations are used either to compute good starting points or to solve subproblems. We present a globally convergent multilevel trust-region algorithm for bound-constrained nonlinear optimization. |
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10h55- 11h20 |
A Multigrid Method for Calibration of Local Volatility |
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Zaiwen Wen, Columbia University, IEOR, USA Rama Cont, Columbia University, IEOR, USA Donald Goldfarb, Columbia University, IEOR, USA The aim of this paper is to calibrate the volatility function in Dupire's equation from given option prices. This inverse problem can be formulated as a PDE-constrained optimization problem. A multigrid method is presented to explore the hierarchical structures of discretized problems on different levels. Computational examples are presented to demonstrate the efficiency of the proposed method. |
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11h20- 11h45 |
Using Approximate Secant Equations in Multilevel Unconstrained Optimization |
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Serge Gratton, CERFACS, Parallel Algorithms Team, 42, Avenue G. Coriolis, Toulouse Cedex, France, 31057 Vincent Malmedy, Université de Namur, Département de Mathématique , Rempart de la Vierge, Namur, Belgique, 5000 Philippe L. Toint, Université de Namur, Département de Mathématique, Rempart de la Vierge 8, Namur, Belgique, 5000 The properties of multilevel optimization problems can be used to define approximate secant equations, which describe the second-order behaviour of the objective function. We introduce a quasi-Newton method (with a line search) and a nonlinear conjugate gradient method that both take advantage of this new second-order information, and present numerical experiments. |