All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 16 Next

Displaying 301 – 320 of 518

Showing per page

Non-parametric approximation of non-anticipativity constraints in scenario-based multistage stochastic programming

Jean-Sébastien Roy, Arnaud Lenoir (2008)

Kybernetika

We propose two methods to solve multistage stochastic programs when only a (large) finite set of scenarios is available. The usual scenario tree construction to represent non-anticipativity constraints is replaced by alternative discretization schemes coming from non-parametric estimation ideas. In the first method, a penalty term is added to the objective so as to enforce the closeness between decision variables and the Nadaraya–Watson estimation of their conditional expectation. A numerical application...

Numerical analysis for optimal shape design in elliptic boundary value problems

Zdeněk Kestřánek (1988)

Aplikace matematiky

Shape optimization problems are optimal design problems in which the shape of the boundary plays the role of a design, i.e. the unknown part of the problem. Such problems arise in structural mechanics, acoustics, electrostatics, fluid flow and other areas of engineering and applied science. The mathematical theory of such kind of problems has been developed during the last twelve years. Recently the theory has been extended to cover also situations in which the behaviour of the system is governed...

Numerical analysis of some optimal control problems governed by a class of quasilinear elliptic equations

Eduardo Casas, Fredi Tröltzsch (2011)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper, we carry out the numerical analysis of a distributed optimal control problem governed by a quasilinear elliptic equation of non-monotone type. The goal is to prove the strong convergence of the discretization of the problem by finite elements. The main issue is to get error estimates for the discretization of the state equation. One of the difficulties in this analysis is that, in spite of the partial differential equation has a unique solution for any given control, the uniqueness...

Numerical analysis of some optimal control problems governed by a class of quasilinear elliptic equations*

Eduardo Casas, Fredi Tröltzsch (2011)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper, we carry out the numerical analysis of a distributed optimal control problem governed by a quasilinear elliptic equation of non-monotone type. The goal is to prove the strong convergence of the discretization of the problem by finite elements. The main issue is to get error estimates for the discretization of the state equation. One of the difficulties in this analysis is that, in spite of the partial differential equation has a unique solution for any given control, the uniqueness...

Numerical procedure to approximate a singular optimal control problem

Silvia C. Di Marco, Roberto L.V. González (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

In this work we deal with the numerical solution of a Hamilton-Jacobi-Bellman (HJB) equation with infinitely many solutions. To compute the maximal solution – the optimal cost of the original optimal control problem – we present a complete discrete method based on the use of some finite elements and penalization techniques.

Numerical realization of a fictitious domain approach used in shape optimization. Part I: Distributed controls

Jana Daňková, Jaroslav Haslinger (1996)

Applications of Mathematics

We deal with practical aspects of an approach to the numerical realization of optimal shape design problems, which is based on a combination of the fictitious domain method with the optimal control approach. Introducing a new control variable in the right-hand side of the state problem, the original problem is transformed into a new one, where all the calculations are performed on a fixed domain. Some model examples are presented.

Numerical resolution of an “unbalanced” mass transport problem

Jean-David Benamou (2003)

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

We introduce a modification of the Monge–Kantorovitch problem of exponent 2 which accommodates non balanced initial and final densities. The augmented lagrangian numerical method introduced in [6] is adapted to this “unbalanced” problem. We illustrate the usability of this method on an idealized error estimation problem in meteorology.

Numerical resolution of an “unbalanced” mass transport problem

Jean-David Benamou (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We introduce a modification of the Monge–Kantorovitch problem of exponent 2 which accommodates non balanced initial and final densities. The augmented Lagrangian numerical method introduced in [6] is adapted to this “unbalanced” problem. We illustrate the usability of this method on an idealized error estimation problem in meteorology.

Numerical study of discretizations of multistage stochastic programs

Petri Hilli, Teemu Pennanen (2008)

Kybernetika

This paper presents a numerical study of a deterministic discretization procedure for multistage stochastic programs where the underlying stochastic process has a continuous probability distribution. The discretization procedure is based on quasi-Monte Carlo techniques originally developed for numerical multivariate integration. The solutions of the discretized problems are evaluated by statistical bounds obtained from random sample average approximations and out-of-sample simulations. In the numerical...

On an optimal control problem for a quasilinear parabolic equation

S. Farag, M. Farag (2000)

Applicationes Mathematicae

An optimal control problem governed by a quasilinear parabolic equation with additional constraints is investigated. The optimal control problem is converted to an optimization problem which is solved using a penalty function technique. The existence and uniqueness theorems are investigated. The derivation of formulae for the gradient of the modified function is explainedby solving the adjoint problem.

On existence of solutions to degenerate nonlinear optimization problems

Agnieszka Prusińska, Alexey Tret'yakov (2007)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

We investigate the existence of the solution to the following problem min φ(x) subject to G(x)=0, where φ: X → ℝ, G: X → Y and X,Y are Banach spaces. The question of existence is considered in a neighborhood of such point x₀ that the Hessian of the Lagrange function is degenerate. There was obtained an approximation for the distance of solution x* to the initial point x₀.

On integral representation, relaxation and homogenization for unbounded functionals

Luciano Carbone, Riccardo De Arcangelis (1997)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

A theory of integral representation, relaxation and homogenization for some types of variational functionals taking extended real values and possibly being not finite also on large classes of regular functions is presented. Some applications to gradient constrained relaxation and homogenization problems are given.

Currently displaying 301 – 320 of 518