References of "Tossings, Patricia"
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See detailFunctional Analysis and the Finite Element Method
Stainier, Laurent; Tossings, Patricia ULiege

Learning material (2008)

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See detailStructural optimisation of steel frames for industrial applications
Mathonet, V.; Degée, Hervé ULiege; Habraken, Anne ULiege et al

in Proceedings of the Inverse Problems Design and Optimization Symposium (2004)

The paper reports the first results of a work carried out in close collaboration between Astron Buildings SA, a manufacturer of industrial steel buildings, and different groups of civil engineers and ... [more ▼]

The paper reports the first results of a work carried out in close collaboration between Astron Buildings SA, a manufacturer of industrial steel buildings, and different groups of civil engineers and mathematicians of the University of Liège to develop an automatic design method for structures with tapered members. This research aims at improving the current method of trialerror followed by experienced engineers to optimize the frames constrained by a chosen national construction code and the technological constraints of the producer. The main benefit of this collaboration arises through the application of a mathematical algorithm based on the sequential quadratic programming method (SQP) in order to reduce, in the first step, the weight of the building, under the great number of constraints. The second step, not yet started, will be devoted to the minimization of the real cost of the frame. This report introduces the first results of this industrial application. [less ▲]

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See detailA trust region algorithm for automatic identification of elasto-viscoplastic model parameters in metallurgical finite element model
Jeunechamps, Pierre-Paul ULiege; Walmag, Jérôme; Duysinx, Pierre ULiege et al

in Steel Grips 2 (2004), Supplement Metal Forming 2004

Simulation of manufacturing processes, here metal forming, has made major progresses during the last years. The virtual simulation of the manufacturing process being now quite well established, a natural ... [more ▼]

Simulation of manufacturing processes, here metal forming, has made major progresses during the last years. The virtual simulation of the manufacturing process being now quite well established, a natural step ahead consists in trying to find automatic procedures to optimize it. Another perspective is also to take care of the influence of the manufacturing constraints upon the design, which is the long term objective of the present research project. It aims at optimizing the design subject to both service constraints (stiffness and strength) and manufacturing constraints. A preliminary stage is to be able to build high fidelity digital models. Complex models require more and more material parameters for behavior laws (e.g. material constitutive and friction laws), which have to be identified numerically from experimental data. In this material parameter identification process, three steps can be identified. At first, an experimental testing is carried out. The second step consists in building a simulation model of the experiment. Finally, the unknown model parameters are determined to match the experimental data. A standard identification procedure consists in minimizing a given norm (here the Euclidean norm) of the error between the model predictions and the experimental results. Even if the identification problem is generally quasi-unconstrained, it has the same complexity as structural optimization problems because of the highly nonlinear and implicit character of the functions, which is especially amplified by the large deformation simulation analysis. In this paper, we use an approach of elastoplastic calculation by finite elements combined with two optimization algorithms: a Levenberg-Marquardt algorithm, which is rather classical in the literature for solving identification problems (see [2]) and a trust-region one (see [1]), which is a rather novel approach at least for structural problems. The results obtained with these two methods are then compared and discussed on two test cases. The first application is an academic test case to validate the identification method. The second one, the compression of a cylinder, takes into account an actual experiment. In this application, the material is assumed to be elasto-viscoplastic and described by a Norton-Hoff behavior law and an isotropic strain hardening law. The parameters to be identified are the coefficients of the Norton-Hoff law. [less ▲]

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See detailIdentification of elastoplastic model in large deformation problems
Jeunechamps, Pierre-Paul ULiege; Walmag, Jérôme ULiege; Delhez, Eric ULiege 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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See detailIdentification of elastoplastic model parameters in large deformation problems using gamma methods
Jeunechamps, Pierre-Paul ULiege; Walmag, J.; Mathonet, V. et al

in Proceedings of the 5th World Congress on Structural and Multidisciplinary Optimization (2003)

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 actuel experiment. [less ▲]

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See detailThe Perturbed Tikhonov's Algorithm with Nonquadratic Kernel and some of its Applications
Brohé, Myrana; Tossings, Patricia ULiege

E-print/Working paper (2001)

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See detailGradient-Proximal like Method for minimizing a Sum of two Convex Functions
Brohé, Myrana; Tossings, Patricia ULiege

E-print/Working paper (2001)

For solving the convex optimization problem of finding a minimizer of a sum of two proper closed convex functions on a real Hilbert space, we consider a sequence generated by an inexact iterative scheme ... [more ▼]

For solving the convex optimization problem of finding a minimizer of a sum of two proper closed convex functions on a real Hilbert space, we consider a sequence generated by an inexact iterative scheme, based upon the Moreau-Yosida approximation, in which the quadratic kernel is replaced by a pseudo-distance, tied to Bregman functions. Several classical results (obtained for the Moreau-Yosida approximation) are extended to this context. [less ▲]

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See detailForward-Backward Method with Nonquadratic Kernel for finding a Zero of a Sum of two Maximal Monotone Operators
Brohé, Myrana; Tossings, Patricia ULiege

E-print/Working paper (2001)

An extension of the (nonexact-perturbed) forward-backward method for finding a zero of a sum of two maximal monotone operators is proposed, using a nonlinear metric, tied to Bregman functions. Results of ... [more ▼]

An extension of the (nonexact-perturbed) forward-backward method for finding a zero of a sum of two maximal monotone operators is proposed, using a nonlinear metric, tied to Bregman functions. Results of weak and strong convergence for a sequence generated by such a method are established, under similar assumptions to those appearing in the context of the proximal point algorithm. [less ▲]

Detailed reference viewed: 50 (2 ULiège)
See detailApplications of the Proximal Point Algorithm with nonquadratic Kernel to Convex Programming
Brohé, Myrana; Tossings, Patricia ULiege

E-print/Working paper (2000)

The proximal point algorithm with nonquadratic kernel is used for solving convex programming problems on a finite dimensional Hilbert space. Dual and primal-dual problems are solved by using aumented ... [more ▼]

The proximal point algorithm with nonquadratic kernel is used for solving convex programming problems on a finite dimensional Hilbert space. Dual and primal-dual problems are solved by using aumented lagrangians. [less ▲]

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See detailOPTIMIZATION: Proceedings of the 9th Belgian-French-German Conference on Optimization, Namur, September 7-11, 1998
Nguyen, Van Hien; Strodiot, Jean-Jacques; Tossings, Patricia ULiege

Book published by Springer (2000)

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See detailPerturbed Proximal Point Algorithm with Nonquadratic Kernel
Brohé, Myrana; Tossings, Patricia ULiege

in Serdica Mathematical Journal (2000), 26

Let H be a real Hilbert space and T be a maximal monotone operator on H. A well-known algorithm, developed by R.T. Rockafellar, for solving the problem "To find x in H such that 0 in Tx" is the proximal ... [more ▼]

Let H be a real Hilbert space and T be a maximal monotone operator on H. A well-known algorithm, developed by R.T. Rockafellar, for solving the problem "To find x in H such that 0 in Tx" is the proximal point algorithm. Several genaralizations have been considered by several authors: introduction of a perturbation, introduction of a variable metric in the perturbed algorithm, introduction of a pseudo-metric in place of the classical regularization, ... We summarize some of these extensions by taking into account a pseudo-metric as regularization and a perturbation in an inexact version of the algorithm. [less ▲]

Detailed reference viewed: 27 (1 ULiège)
See detailRelaxed Assumptions for Iteration Methods
Brohé, Myrana; Tossings, Patricia ULiege

E-print/Working paper (1999)

We consider a general inexact iterative method for finding a fixed point of a nonexpansive mapping on a real Hilbert space. Proofs of convergence of sequences generated by such a method generally require ... [more ▼]

We consider a general inexact iterative method for finding a fixed point of a nonexpansive mapping on a real Hilbert space. Proofs of convergence of sequences generated by such a method generally require that the error term goes to zero. The aim of the present paper is to weaken this nonrealistic theoretical assumption. The obtained results are applied to the proximal point algorithm. [less ▲]

Detailed reference viewed: 38 (5 ULiège)
See detailPerturbed Proximal Point Algorithm with Nonquadratic Kernel
Brohé, Myrana; Tossings, Patricia ULiege

E-print/Working paper (1998)

Let H be a real Hilbert space and T be a maximal monotone operator on H. A well-known algorithm, developed by R.T. Rockafellar, for solving the problem "To find x in H such that 0 in Tx" is the proximal ... [more ▼]

Let H be a real Hilbert space and T be a maximal monotone operator on H. A well-known algorithm, developed by R.T. Rockafellar, for solving the problem "To find x in H such that 0 in Tx" is the proximal point algorithm. Several generalizations have been considered by several authors: introduction of a perturbation, introduction of a variable metric in the perturbed algorithm, introduction of a pseudo-metric in place of the classical regularization, ... We summarize several of these extensions by taking into account a pseudo-metric as regularization and a perturbation in an inexact version of the algorithm. [less ▲]

Detailed reference viewed: 35 (2 ULiège)
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See detailRelaxed Assumptions for Iteration Methods
Brohé, Myrana; Tossings, Patricia ULiege

in Nguyen, Van Hien; Strodiot, Jean-Jacques; Tossings, Patricia (Eds.) OPTIMIZATION (V.H. Nguyen - J.J. Strodiot - P. Tossings Editors), Proceedings BFG, Namur (1998)

We consider a general inexact interative method for finding a fixed point of a nonexpansive mapping on a real Hilbert space. Proofs of convergence of sequences generated by such a method generally require ... [more ▼]

We consider a general inexact interative method for finding a fixed point of a nonexpansive mapping on a real Hilbert space. Proofs of convergence of sequences generated by such a method generally require at least that the error term goes to zero. The aim of the present paper is to weaken this nonrealistic theoretical assumption. The obtained result is applied to the proximal point algorithm. [less ▲]

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See detailThe Perturbed Generalized Proximal Point Algorithm
Alexandre, Patrick; Nguyen, Van Hien; Tossings, Patricia ULiege

in Mathematical Modelling and Numerical Analysis (1998), 32(2), 223-253

During the last years, different modifications were introduced in the proximal point algorithm devloped by R.T. Rockafellar for searching a zero of a maximal monotone operator on a real Hilbert space. We ... [more ▼]

During the last years, different modifications were introduced in the proximal point algorithm devloped by R.T. Rockafellar for searching a zero of a maximal monotone operator on a real Hilbert space. We combine these modifications to get a new version of this algorithm. We take simultaneously into account a variable metric, a perturbation and a kind of relaxation. Our work takes place in the context of the variational convergence theory. [less ▲]

Detailed reference viewed: 30 (0 ULiège)
See detailFonctions d'une variable réelle
Tossings, Patricia ULiege

Learning material (1997)

Detailed reference viewed: 55 (5 ULiège)
See detailThe Generalized Variational Metric
Alexandre, Patrick; Tossings, Patricia ULiege

E-print/Working paper (1996)

The variational convergence theory has known these last years a lot of developments. This theory is fundamental to give a global approach of problems which consist in searching a zero of a maximal ... [more ▼]

The variational convergence theory has known these last years a lot of developments. This theory is fundamental to give a global approach of problems which consist in searching a zero of a maximal monotone operator on a real Hilbert space. The notion of perturbation is often used in the resolution of such problems. More and more authors work also with a special or a variable metric on the space to solve this kind of problems. In the present paper, we give a unified context to couple these two approaches: a variational metric between operators, taking into account different metrics on the space. [less ▲]

Detailed reference viewed: 52 (1 ULiège)
See detailThe Perturbed Generalized Proximal Point Algorithm
Alexandre, Patrick; Nguyen, Van Hien; Tossings, Patricia ULiege

E-print/Working paper (1996)

During the last years, different modifications were introduced in the proximal point algorithm developed by R.T. Rockafellar for searching a zero of a maximal monotone operator on a real Hilbert space. We ... [more ▼]

During the last years, different modifications were introduced in the proximal point algorithm developed by R.T. Rockafellar for searching a zero of a maximal monotone operator on a real Hilbert space. We combine these modifications to get a new version of this algorithm. We take simultaneously into account a variable metric, a perturbation and a kind of relaxation. Our work takes place in the context of the variational convergence theory. [less ▲]

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See detailThe Perturbed Proximal Point Algorithm and Some of its Applications
Tossings, Patricia ULiege

in Applied Mathematics and Optimization (1994), 29(2), 125-159

Following the works of R.T. Rockafellar, to search for a zero of a maximal monotone operator, and of B. Lemaire, to solve convex optimization problems, we present a perturbed version of the proximal point ... [more ▼]

Following the works of R.T. Rockafellar, to search for a zero of a maximal monotone operator, and of B. Lemaire, to solve convex optimization problems, we present a perturbed version of the proximal point algorithm. We apply this new algorithm to convex optimization and to variational inclusions or, more particularly, to variational inequalities. [less ▲]

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