Generalized quasi-variational inequalities and duality.
Geometric convergence of iterative methods for variational inequalities with -matrices and diagonal monotone operators
Graphical model selection for a particular class of continuous-time processes
Graphical models provide an undirected graph representation of relations between the components of a random vector. In the Gaussian case such an undirected graph is used to describe conditional independence relations among such components. In this paper, we consider a continuous-time Gaussian model which is accessible to observations only at time . We introduce the concept of infinitesimal conditional independence for such a model. Then, we address the corresponding graphical model selection problem,...
Hamiltonian identification for quantum systems: well-posedness and numerical approaches
This paper considers the inversion problem related to the manipulation of quantum systems using laser-matter interactions. The focus is on the identification of the field free Hamiltonian and/or the dipole moment of a quantum system. The evolution of the system is given by the Schrödinger equation. The available data are observations as a function of time corresponding to dynamics generated by electric fields. The well-posedness of the problem is proved, mainly focusing on the uniqueness of the...
Heat exposure optimization applied to moulding process in the automotive industry
This contribution contains a description and comparison of two methods applied to exposure optimization applied to moulding process in the automotive industry.
Hemiequilibrium problems.
Hierarchical control via augmented Lagrangians
How to avoid the use of Green's theorem in the Ciarlet-Raviart theory of variational crimes
Identification of basic thermal technical characteristics of building materials
Modelling of building heat transfer needs two basic material characteristics: heat conduction factor and thermal capacity. Under some simplifications these two factors can be determined from a rather simple equipment, generating heat from one of two aluminium plates into the material sample and recording temperature on the contacts between the sample and the plates. However, the numerical evaluation of both characteristics leads to a non-trivial optimization problem. This article suggests an efficient...
Image segmentation with a finite element method
Image segmentation with a finite element method
The Mumford-Shah functional for image segmentation is an original approach of the image segmentation problem, based on a minimal energy criterion. Its minimization can be seen as a free discontinuity problem and is based on Γ-convergence and bounded variation functions theories. Some new regularization results, make possible to imagine a finite element resolution method. In a first time, the Mumford-Shah functional is introduced and some existing results are quoted. Then, a discrete formulation...
Improved local convergence analysis of inexact Newton-like methods under the majorant condition
We present a local convergence analysis of inexact Newton-like methods for solving nonlinear equations. Using more precise majorant conditions than in earlier studies, we provide: a larger radius of convergence; tighter error estimates on the distances involved; and a clearer relationship between the majorant function and the associated least squares problem. Moreover, these advantages are obtained under the same computational cost.
Inequality-based approximation of matrix eigenvectors
A novel procedure is given here for constructing non-negative functions with zero-valued global minima coinciding with eigenvectors of a general real matrix A. Some of these functions are distinct because all their local minima are also global, offering a new way of determining eigenpairs by local optimization. Apart from describing the framework of the method, the error bounds given separately for the approximation of eigenvectors and eigenvalues provide a deeper insight into the fundamentally...
Internal approximation of quasi-variational inequalities.
Inverse coefficient problems for variational inequalities : optimality conditions and numerical realization
We consider the identification of a distributed parameter in an elliptic variational inequality. On the basis of an optimal control problem formulation, the application of a primal-dual penalization technique enables us to prove the existence of multipliers giving a first order characterization of the optimal solution. Concerning the parameter we consider different regularity requirements. For the numerical realization we utilize a complementarity function, which allows us to rewrite the optimality...
Inverse Coefficient Problems for Variational Inequalities: Optimality Conditions and Numerical Realization
We consider the identification of a distributed parameter in an elliptic variational inequality. On the basis of an optimal control problem formulation, the application of a primal-dual penalization technique enables us to prove the existence of multipliers giving a first order characterization of the optimal solution. Concerning the parameter we consider different regularity requirements. For the numerical realization we utilize a complementarity function, which allows us to rewrite the optimality...
Iterative algorithm for solving mixed quasi-variational-like inequalities with skew-symmetric terms in Banach spaces.
Iterative methods for nonlinear quasi complementarity problems.
Iterative methods for solving the dual formulation arising from image restoration.
Iterative solution of unstable variational inequalities on approximately given sets.