Publication detail

Different Reformulations of Stochastic Optimization of the Transverse Vibration

ŽAMPACHOVÁ, E. POPELA, P.

Czech title

Reformulace úloh stochastické optimalizace příčného kmitání

English title

Different Reformulations of Stochastic Optimization of the Transverse Vibration

Type

journal article - other

Language

en

Original abstract

The applicability of stochastic programming models and methods to PDE constrained stochastic optimization problem is discussed. The problem concerning the transverse vibration of a string is chosen. Therefore, the corresponding mathematical model involves a PDE-type constraint and an uncertain parameter related to the external load. A computational scheme for this type of problems is proposed, including discretization methods for random elements (scenario based two-stage stochastic programming) and the PDE constraint (finite difference method). Several deterministic reformulations are presented and compared using numerical and graphical results.

Czech abstract

Je diskutována použitelnost modelů a metod stochastického programování na úloze s PDR omezením popisující příčné kmitání struny zatížené náhodně. Je navrženo výpočtové schéma pro tento typ úloh zahrnující diskretizační metody pro náhodné elementy a PDR omezení. Je srovnáno několik typů deterministických reformulací pomocí numerických a grafických výsledků.

English abstract

The applicability of stochastic programming models and methods to PDE constrained stochastic optimization problem is discussed. The problem concerning the transverse vibration of a string is chosen. Therefore, the corresponding mathematical model involves a PDE-type constraint and an uncertain parameter related to the external load. A computational scheme for this type of problems is proposed, including discretization methods for random elements (scenario based two-stage stochastic programming) and the PDE constraint (finite difference method). Several deterministic reformulations are presented and compared using numerical and graphical results.

Keywords in Czech

stochastické programování, parciální diferenciální rovnice, metoda konečných diferencí

Keywords in English

stochastic programming, PDE, finite difference method

RIV year

2011

Released

01.02.2011

Publisher

FSI VUT Brno

Location

Brno

ISSN

1802-1484

Journal

Engineering Mechanics

Volume

17

Number

5/6

Pages from–to

339–350

Pages count

12

BIBTEX


@article{BUT49990,
  author="Eva {Mrázková} and Pavel {Popela},
  title="Different Reformulations of Stochastic Optimization of the Transverse Vibration",
  journal="Engineering Mechanics",
  year="2011",
  volume="17",
  number="5/6",
  month="February",
  pages="339--350",
  publisher="FSI VUT Brno",
  address="Brno",
  issn="1802-1484"
}