A two-stage stochastic program with elliptic pde constraints
Result description
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 variousapplications 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 m
Keywords
Finite difference methodGAMSMembrane designMonte CarloPartial differential equation constraintScenariosTwo-stage stochastic programming
The result's identifiers
Result code in IS VaVaI
Result on the web
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DOI - Digital Object Identifier
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Alternative languages
Result language
angličtina
Original language name
A two-stage stochastic program with elliptic pde constraints
Original language description
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 variousapplications 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 m
Czech name
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Czech description
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Classification
Type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BB - Applied statistics, operational research
OECD FORD branch
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Result continuities
Project
1M06047: Research Center for Quality and Reliability of Production
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2010
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Mendel Journal series
ISSN
1803-3814
e-ISSN
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Volume of the periodical
2010
Issue of the periodical within the volume
1
Country of publishing house
CZ - CZECH REPUBLIC
Number of pages
6
Pages from-to
447-452
UT code for WoS article
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EID of the result in the Scopus database
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Basic information
Result type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP
BB - Applied statistics, operational research
Year of implementation
2010