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Application of relaxation scheme to degenerate variational inequalities

Jela Babušíková (2001)

Applications of Mathematics

In this paper we are concerned with the solution of degenerate variational inequalities. To solve this problem numerically, we propose a numerical scheme which is based on the relaxation scheme using non-standard time discretization. The approximate solution on each time level is obtained in the iterative way by solving the corresponding elliptic variational inequalities. The convergence of the method is proved.

Application of the infinitely many times repeated BNS update and conjugate directions to limited-memory optimization methods

Vlček, Jan, Lukšan, Ladislav (2019)

Programs and Algorithms of Numerical Mathematics

To improve the performance of the L-BFGS method for large scale unconstrained optimization, repeating of some BFGS updates was proposed e.g. in [1]. Since this can be time consuming, the extra updates need to be selected carefully. We show that groups of these updates can be repeated infinitely many times under some conditions, without a noticeable increase of the computational time; the limit update is a block BFGS update [17]. It can be obtained by solving of some Lyapunov matrix equation whose...

Approximation of maximal Cheeger sets by projection

Guillaume Carlier, Myriam Comte, Gabriel Peyré (2009)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

This article deals with the numerical computation of the Cheeger constant and the approximation of the maximal Cheeger set of a given subset of ℝ d . This problem is motivated by landslide modelling as well as by the continuous maximal flow problem. Using the fact that the maximal Cheeger set can be approximated by solving a rather simple projection problem, we propose a numerical strategy to compute maximal Cheeger sets and Cheeger constants.

Approximation of maximal Cheeger sets by projection

Guillaume Carlier, Myriam Comte, Gabriel Peyré (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

This article deals with the numerical computation of the Cheeger constant and the approximation of the maximal Cheeger set of a given subset of ℝ d . This problem is motivated by landslide modelling as well as by the continuous maximal flow problem. Using the fact that the maximal Cheeger set can be approximated by solving a rather simple projection problem, we propose a numerical strategy to compute maximal Cheeger sets and Cheeger constants.

Approximations of parabolic variational inequalities

Alexander Ženíšek (1985)

Aplikace matematiky

The paper deals with an initial problem of a parabolic variational inequality whichcontains a nonlinear elliptic form a ( v , w ) having a potential J ( v ) , which is twice G -differentiable at arbitrary v ∈ H 1 ( Ω ) . This property of a ( v , w ) makes it possible to prove convergence of an approximate solution defined by a linearized scheme which is fully discretized - in space by the finite elements method and in time by a one-step finite-difference method. Strong convergence of the approximate solution is proved without any regularity...

Bilevel Approach of a Decomposed Topology Optimization Problem

A. Makrizi, B. Radi (2010)

Mathematical Modelling of Natural Phenomena

In topology optimization problems, we are often forced to deal with large-scale numerical problems, so that the domain decomposition method occurs naturally. Consider a typical topology optimization problem, the minimum compliance problem of a linear isotropic elastic continuum structure, in which the constraints are the partial differential equations of linear elasticity. We subdivide the partial differential equations into two subproblems posed...

Biochemical network of drug-induced enzyme production: Parameter estimation based on the periodic dosing response measurement

Volodymyr Lynnyk, Štěpán Papáček, Branislav Rehák (2021)

Kybernetika

The well-known bottleneck of systems pharmacology, i. e., systems biology applied to pharmacology, refers to the model parameters determination from experimentally measured datasets. This paper represents the development of our earlier studies devoted to inverse (ill-posed) problems of model parameters identification. The key feature of this research is the introduction of control (or periodic forcing by an input signal being a drug intake) of the nonlinear model of drug-induced enzyme production...

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