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See detailOptimisation contrainte et non-contrainte par régions de confiance avec approximations locales quadratiques
Walmag, Jérôme ULg

Doctoral thesis (2011)

This work deals with optimisation problems in which the numerical cost associated with the evaluation of the target function and/or of the constraints is large; the number of calls to these functions by ... [more ▼]

This work deals with optimisation problems in which the numerical cost associated with the evaluation of the target function and/or of the constraints is large; the number of calls to these functions by the optimisation algorithm should therefore be kept as small as possible. The first part of the work is about globalisation by trust regions where the objective function and the constraints are replaced by a local approximation, easier to use, in a certain region of confidence. Different types of local approximations are introduced but the main part of the work deals with quadratic approximations. The theoretical aspects of the global convergence of trust regions methods are also presented. One of the applications considered in this work is the parametrical identification of a dynamical model with respect to experimental measurements. This identification can be expressed in the form of an unconstrained optimisation problem. For the practical implementation of the identification algorithm, the derivative of the objective function is required, which asks for the derivation of the underlying model. An algorithm, named Trust, has been implemented: it is a trust region method of quasi-Newton type which uses quadratic local approximations. The choice of the differentiation method is analysed in details in relation with its influence on the rate of convergence. A brand new update strategy of the trust region radius is also introduced. The trust region radius is a parameter that measures the size of the trust region around the current iterate. The new approach relies on the identification and appropriate handling of so-called “too successful iterations” that lead to a much more important reduction of the function objective than predicted by the local approximation. This approach goes with a significant improvement of the performances of the algorithm. Constrained optimisation is then considered using sequential quadratic methods. A fully effective algorithm for the resolution of quadratic convex sub-problems with quadratic constraints is introduced. This original method, named UVQCQP, makes use of an exact non-differentiable penalty function to addresses the constrained optimisation problem. The algorithm relies on a decomposition of the variable space into three orthogonal subspaces: a first subspace taking into account bound constraints, a second one in which the objective function is continuously derivable and a third one with slope discontinuities. The performances of this algorithm are further improved by the implementation of a fast mode taking into account the second order corrections. Eventually, the UVQCQP algorithm is applied within the framework of sequential algorithms of quadratic programming with quadratic constraints: its advantages are demonstrated through some examples. The numerical tests carried out reveal very encouraging prospects. [less ▲]

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See detailIdentification of elastoplastic model in large deformation problems
Jeunechamps, Pierre-Paul ULg; Walmag, Jérôme ULg; Delhez, Eric ULg et al

in Cinquini, Carlo (Ed.) Proceedings of the 5th World Congress of Structural and Multidisciplinary Optimization WCSMO5 (2003, May)

This paper reports on preliminary results of parameter identification problems in finite element non-linear analyses such as metal forming simulations. Two approaches are compared. The first one is the ... [more ▼]

This paper reports on preliminary results of parameter identification problems in finite element non-linear analyses such as metal forming simulations. Two approaches are compared. The first one is the classic Levenberg-Marquardt algorithm. The second one is a trust-region algorithm based on a quadratic model. The two algorithms are compared on two cases, one of them being an actual experiment. [less ▲]

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