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Some dynamical systems are characterized by more than one time-scale, e.g. two well separated time-scales are typical for quasiperiodic systems. The aim of this paper is to show how singular perturbation methods based on the slow-fast decomposition can serve for an enhanced parameter estimation when the slowly changing features are rigorously treated. Although the ultimate goal is to reduce the standard error for the estimated parameters, here we test two methods for numerical approximations of...
For the symmetric Pareto Eigenvalue Complementarity Problem (EiCP), by reformulating it as a constrained optimization problem on a differentiable Rayleigh quotient function, we present a class of descent methods and prove their convergence. The main features include: using nonlinear complementarity functions (NCP functions) and Rayleigh quotient gradient as the descent direction, and determining the step size with exact linear search. In addition, these algorithms are further extended to solve the...
Searching for the optimal partitioning of a domain leads to the use of the adjoint method in topological asymptotic expansions to know the influence of a domain perturbation on a cost function. Our approach works by restricting to local subproblems containing the perturbation and outperforms the adjoint method by providing approximations of higher order. It is a universal tool, easily adapted to different kinds of real problems and does not need the fundamental solution of the problem; furthermore...
Searching for the optimal partitioning of a domain leads to the use of the adjoint method
in topological asymptotic expansions to know the influence of a domain perturbation on a
cost function. Our approach works by restricting to local subproblems containing the
perturbation and outperforms the adjoint method by providing approximations of higher
order. It is a universal tool, easily adapted to different kinds of real problems and does
not need...
A gradient method for solving an optimal control problem described by a parabolic equation is considered. The gradient projection method is applied to solve the problem. The convergence of the projection algorithm is investigated.
We study a parameter (σ)
dependent relaxation of the Travelling Salesman Problem on .
The relaxed problem is reduced to the Travelling Salesman Problem
as 0. For increasing σ it is also an
ordered clustering algorithm for a set of points in .
A dual formulation is introduced, which reduces the problem to a
convex optimization, provided the minimizer is in the domain of
convexity of the relaxed functional. It is shown that this last
condition is generically satisfied, provided σ is large
enough.
...
This paper deals with the flow problem of a viscous plastic fluid in a cylindrical pipe. In order to approximate this problem governed by a variational inequality, we apply the nonconforming mortar finite element method. By using appropriate techniques, we are able to prove the convergence of the method and to obtain the same convergence rate as in the conforming case.
This paper deals with the flow problem of a
viscous plastic fluid in a cylindrical pipe. In order to
approximate this problem governed by a variational inequality, we
apply the nonconforming
mortar finite element method. By using
appropriate techniques, we are able to prove the convergence of the method
and to obtain the same convergence rate as in the conforming case.
This article focuses on the problem of calculating the intensity of heat radiation and its optimization across the surface of an aluminium or nickel mould. The inner mould surface is sprinkled with a special PVC powder and the outer mould surface is warmed by infrared heaters located above the mould. In this way artificial leathers are produced in the car industry (e.g., the artificial leather on a car dashboard). The article includes a description of how a mathematical model allows us to calculate
the...
The soil water movement model governed by the initial-boundary value problem for a quasilinear 1-D parabolic equation with nonlinear coefficients is considered. The generalized statement of the problem is formulated. The solvability of the problem is proved in a certain class of functional spaces. The data assimilation problem for this model is analysed. The numerical results are presented.
The soil water movement model
governed by the initial-boundary value problem for a quasilinear
1-D parabolic equation with nonlinear coefficients is considered.
The generalized statement of the problem is formulated. The
solvability of the problem is proved in a certain class of
functional spaces. The data assimilation problem for this model is
analysed. The numerical results are presented.
The motivation of this article is double. First of all we provide a geometrical framework to the application of the smooth continuation method in optimal control, where the concept of conjugate points is related to the convergence of the method. In particular, it can be applied to the analysis of the global optimality properties of the geodesic flows of a family of Riemannian metrics. Secondly, this study is used to complete the analysis of two-level dissipative quantum systems, where the system...
The motivation of this article is double. First of all we provide a geometrical framework to the application of the smooth continuation method in optimal control, where the concept of conjugate points is related to the convergence of the method. In particular, it can be applied to the analysis of the global optimality properties of the geodesic flows of a family of Riemannian metrics. Secondly, this study is used to complete the analysis of two-level dissipative quantum systems, where the system...
Wireless LAN using IEEE 802.11 networks are now widely deployed at home by residential users or in hot spots by telecommunication operators. A hot spot is a place where a set of access points (APs) are located nearby each other and can serve many users. Since perturbations can degrade the quality of the signal, a careful channel assignment to each AP has to be done. Channel assignment of APs at hot spots, and more generally setup configuration and management, is still often done manually. In this...
Wireless LAN using IEEE 802.11 networks are now widely deployed at
home by residential users or in hot spots by telecommunication
operators. A hot spot is a place where a set of access points (APs)
are located nearby each other and can serve many users. Since
perturbations can degrade the quality of the signal, a careful
channel assignment to each AP has to be done. Channel assignment of
APs at hot spots, and more generally setup configuration and
management, is still often done manually. In this...
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