Reduced-basis techniques for rapid reliable optimization of systems described by affinely parametrized coercive elliptic partial differential equations

DOI10.1007/s11081-007-9002-6zbMath1171.65404OpenAlexW2060637820MaRDI QIDQ1027156

I. B. Oliveira, Anthony T. Patera

Publication date: 30 June 2009

Published in: Optimization and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11081-007-9002-6

zbMATH Keywords

heat transferLaplace equationoptimal designa posteriori error estimationengineering optimizationparametrized partial differential equationsreal-time computinguncertainty controloutput boundsreduced-basis approximation

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Existence theories for optimal control problems involving partial differential equations (49J20) Finite difference methods applied to problems in thermodynamics and heat transfer (80M20) Discrete approximations in optimal control (49M25)

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Uses Software

• rSQP++
• SNOPT

Cites Work

• A reduced-order method for simulation and control of fluid flows
• A priori convergence theory for reduced-basis approximations of single-parameter elliptic partial differential equations
• An `empirical interpolation' method: Application to efficient reduced-basis discretization of partial differential equations
• On the Error Behavior of the Reduced Basis Technique for Nonlinear Finite Element Approximations
• Estimation of the Error in the Reduced Basis Method Solution of Nonlinear Equations
• Primal-Dual Interior Methods for Nonconvex Nonlinear Programming
• A PosterioriError Estimation for Reduced-Basis Approximation of Parametrized Elliptic Coercive Partial Differential Equations: “Convex Inverse” Bound Conditioners
• A Mathematical and Computational Framework for Reliable Real-Time Solution of Parametrized Partial Differential Equations
• Output bounds for reduced-basis approximations of symmetric positive definite eigenvalue problems
• Certified real‐time solution of the parametrized steady incompressible Navier–Stokes equations: rigorous reduced‐basis a posteriori error bounds
• An Interior Point Algorithm for Large-Scale Nonlinear Programming
• SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization
• Interior Methods for Nonlinear Optimization
• On the Reduced Basis Method
• Parallel Lagrange--Newton--Krylov--Schur Methods for PDE-Constrained Optimization. Part I: The Krylov--Schur Solver
• Elements of structural optimization.
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