Detail publikace
A two-stage stochastic program with elliptic pde constraints
POPELA, P. ČAJÁNEK, M.
Anglický název
A two-stage stochastic program with elliptic pde constraints
Typ
Článek recenzovaný mimo WoS a Scopus
Jazyk
en
Originální abstrakt
The purpose of the paper is to introduce an optimization model for a problem involving random elements and constraints formed by an elliptic partial differential equation and related conditions. The discussed problem may serve as a prototype for various applications in mechanical and civil engineering. The problem con- cerning an optimal design of a membrane under a random load has been chosen. The corresponding mathematical model involves a partial differential equation (PDE) type constraint, specifically, the elliptic PDE is considered. It has been shown that the two-stage stochastic programming related scheme offers a promising approach to study similar problems. The formally correct description of the model serves as the initial step towards a computable model. A computational scheme for this type of problems is proposed, including discretization methods to tackle randomness and continuity involved in the formal description. By means of the derived approximation, the mathematical model is detailed, implemented, and solved in GAMS. Then the solution quality is tested by Monte Carlo technique. Finally, the graphical and numerical results are presented and interpreted.
Klíčová slova anglicky
Finite difference method; GAMS; Membrane design; Monte Carlo; Partial differential equation constraint; Scenarios; Two-stage stochastic programming
Vydáno
2010-06-22
ISBN
978-80-214-4120-0
ISSN
1803-3814
Kniha
Conference Proceedings Mendel 2010
Časopis
Mendel Journal series
Ročník
2010
Číslo
1
Strany od–do
447–452
Počet stran
6
BIBTEX
@article{BUT124323,
author="Pavel {Popela} and Michal {Čajánek}",
title="A two-stage stochastic program with elliptic pde constraints",
journal="Mendel Journal series",
year="2010",
volume="2010",
number="1",
pages="447--452",
issn="1803-3814"
}