Detail publikace

Dvoustupňový stochastický program s omezeními ve tvaru eliptické PDR

POPELA, P. ČAJÁNEK, M.

Český název

Dvoustupňový stochastický program s omezeními ve tvaru eliptické PDR

Anglický název

A two-stage stochastic program with elliptic pde constraints

Typ

článek v časopise - ostatní, Jost

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.

Anglický 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

22.06.2010

ISBN

978-80-214-4120-0

ISSN

1803-3814

Kniha

Conference Proceedings Mendel 2010

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",
  booktitle="Conference Proceedings Mendel 2010",
  year="2010",
  volume="2010",
  number="1",
  month="June",
  pages="447--452",
  isbn="978-80-214-4120-0",
  issn="1803-3814"
}