General algorithm and sensitivity analysis for variational inequalities.
Generalized minimizers of convex integral functionals, Bregman distance, Pythagorean identities
Integral functionals based on convex normal integrands are minimized subject to finitely many moment constraints. The integrands are finite on the positive and infinite on the negative numbers, strictly convex but not necessarily differentiable. The minimization is viewed as a primal problem and studied together with a dual one in the framework of convex duality. The effective domain of the value function is described by a conic core, a modification of the earlier concept of convex core. Minimizers...
Generalized Newton methods for the 2D-Signorini contact problem with friction in function space
The 2D-Signorini contact problem with Tresca and Coulomb friction is discussed in infinite-dimensional Hilbert spaces. First, the problem with given friction (Tresca friction) is considered. It leads to a constraint non-differentiable minimization problem. By means of the Fenchel duality theorem this problem can be transformed into a constrained minimization involving a smooth functional. A regularization technique for the dual problem motivated by augmented lagrangians allows to apply an infinite-dimensional...
Generalized Newton methods for the 2D-Signorini contact problem with friction in function space
The 2D-Signorini contact problem with Tresca and Coulomb friction is discussed in infinite-dimensional Hilbert spaces. First, the problem with given friction (Tresca friction) is considered. It leads to a constraint non-differentiable minimization problem. By means of the Fenchel duality theorem this problem can be transformed into a constrained minimization involving a smooth functional. A regularization technique for the dual problem motivated by augmented Lagrangians allows to apply an...
Generalized quasi-variational inequalities and duality.
Genetic Algorithm Approach for Solving the Task Assignment Problem
This research was partially supported by the Serbian Ministry of Science and Ecology under project 144007. The authors are grateful to Ivana Ljubić for help in testing and to Vladimir Filipović for useful suggestions and comments.In this paper a genetic algorithm (GA) for the task assignment problem (TAP) is considered.An integer representation with standard genetic operators is used. Computational results are presented for instances from the literature, and compared to optimal solutions obtained...
Geometric convergence of iterative methods for variational inequalities with -matrices and diagonal monotone operators
Global convergence of a modified SQP method for mathematical programs with inequalities and equalities constraints.
Global convergence property of modified Levenberg-Marquardt methods for nonsmooth equations
In this paper, we discuss the globalization of some kind of modified Levenberg-Marquardt methods for nonsmooth equations and their applications to nonlinear complementarity problems. In these modified Levenberg-Marquardt methods, only an approximate solution of a linear system at each iteration is required. Under some mild assumptions, the global convergence is shown. Finally, numerical results show that the present methods are promising.
Global Optimization Using Interval Analysis - The Multi-Dimensional Case.
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,...
Greedy algorithms for optimal computing of matrix chain products involving square dense and triangular matrices
This paper addresses a combinatorial optimization problem (COP), namely a variant of the (standard) matrix chain product (MCP) problem where the matrices are square and either dense (i.e. full) or lower/upper triangular. Given a matrix chain of length n, we first present a dynamic programming algorithm (DPA) adapted from the well known standard algorithm and having the same O(n3) complexity. We then design and analyse two optimal O(n) greedy algorithms leading in general to different optimal solutions...
Greedy algorithms for optimal computing of matrix chain products involving square dense and triangular matrices
This paper addresses a combinatorial optimization problem (COP), namely a variant of the (standard) matrix chain product (MCP) problem where the matrices are square and either dense (i.e. full) or lower/upper triangular. Given a matrix chain of length n, we first present a dynamic programming algorithm (DPA) adapted from the well known standard algorithm and having the same O(n3) complexity. We then design and analyse two optimal O(n) greedy algorithms leading in general to different optimal solutions...
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 much do approximate derivatives hurt filter methods?
In this paper, we examine the influence of approximate first and/or second derivatives on the filter-trust-region algorithm designed for solving unconstrained nonlinear optimization problems and proposed by Gould, Sainvitu and Toint in [12]. Numerical experiments carried out on small-scaled unconstrained problems from the CUTEr collection describe the effect of the use of approximate derivatives on the robustness and the efficiency of the filter-trust-region method.
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...