Reliable Real-Time Optimization of Nonconvex Systems Described by Parametrized Partial Differential Equations
The solution of a single optimization problem often requires computationally-demanding evaluations; this is especially true in optimal design of engineering components and systems described by partial differential equations. We present a technique for the rapid and reliable optimization of systems c...
| Main Authors: | , |
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| Format: | Article |
| Language: | en_US |
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2003
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| Online Access: | http://hdl.handle.net/1721.1/3707 |
| _version_ | 1826192081946673152 |
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| author | Oliveira, I.B. Patera, Anthony T. |
| author_facet | Oliveira, I.B. Patera, Anthony T. |
| author_sort | Oliveira, I.B. |
| collection | MIT |
| description | The solution of a single optimization problem often requires computationally-demanding evaluations; this is especially true in optimal design of engineering components and systems described by partial differential equations. We present a technique for the rapid and reliable optimization of systems characterized by linear-functional outputs of partial differential equations with affine parameter dependence. The critical ingredients of the method are: (i) reduced-basis techniques for dimension reduction in computational requirements; (ii) an "off-line/on-line" computational decomposition for the rapid calculation of outputs of interest and respective sensitivities in the limit of many queries; (iii) a posteriori error bounds for rigorous uncertainty and feasibility control; (iv) Interior Point Methods (IPMs) for efficient solution of the optimization problem; and (v) a trust-region Sequential Quadratic Programming (SQP) interpretation of IPMs for treatment of possibly non-convex costs and constraints. |
| first_indexed | 2024-09-23T09:05:59Z |
| format | Article |
| id | mit-1721.1/3707 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T09:05:59Z |
| publishDate | 2003 |
| record_format | dspace |
| spelling | mit-1721.1/37072019-04-10T20:44:53Z Reliable Real-Time Optimization of Nonconvex Systems Described by Parametrized Partial Differential Equations Oliveira, I.B. Patera, Anthony T. parametrized partial differential equations reduced-basis computational decomposition a posteriori error bounds Interior Point Methods Sequential Quadratic Programming The solution of a single optimization problem often requires computationally-demanding evaluations; this is especially true in optimal design of engineering components and systems described by partial differential equations. We present a technique for the rapid and reliable optimization of systems characterized by linear-functional outputs of partial differential equations with affine parameter dependence. The critical ingredients of the method are: (i) reduced-basis techniques for dimension reduction in computational requirements; (ii) an "off-line/on-line" computational decomposition for the rapid calculation of outputs of interest and respective sensitivities in the limit of many queries; (iii) a posteriori error bounds for rigorous uncertainty and feasibility control; (iv) Interior Point Methods (IPMs) for efficient solution of the optimization problem; and (v) a trust-region Sequential Quadratic Programming (SQP) interpretation of IPMs for treatment of possibly non-convex costs and constraints. Singapore-MIT Alliance (SMA) 2003-11-19T20:52:21Z 2003-11-19T20:52:21Z 2003-01 Article http://hdl.handle.net/1721.1/3707 en_US High Performance Computation for Engineered Systems (HPCES); 334725 bytes application/pdf application/pdf |
| spellingShingle | parametrized partial differential equations reduced-basis computational decomposition a posteriori error bounds Interior Point Methods Sequential Quadratic Programming Oliveira, I.B. Patera, Anthony T. Reliable Real-Time Optimization of Nonconvex Systems Described by Parametrized Partial Differential Equations |
| title | Reliable Real-Time Optimization of Nonconvex Systems Described by Parametrized Partial Differential Equations |
| title_full | Reliable Real-Time Optimization of Nonconvex Systems Described by Parametrized Partial Differential Equations |
| title_fullStr | Reliable Real-Time Optimization of Nonconvex Systems Described by Parametrized Partial Differential Equations |
| title_full_unstemmed | Reliable Real-Time Optimization of Nonconvex Systems Described by Parametrized Partial Differential Equations |
| title_short | Reliable Real-Time Optimization of Nonconvex Systems Described by Parametrized Partial Differential Equations |
| title_sort | reliable real time optimization of nonconvex systems described by parametrized partial differential equations |
| topic | parametrized partial differential equations reduced-basis computational decomposition a posteriori error bounds Interior Point Methods Sequential Quadratic Programming |
| url | http://hdl.handle.net/1721.1/3707 |
| work_keys_str_mv | AT oliveiraib reliablerealtimeoptimizationofnonconvexsystemsdescribedbyparametrizedpartialdifferentialequations AT pateraanthonyt reliablerealtimeoptimizationofnonconvexsystemsdescribedbyparametrizedpartialdifferentialequations |