Reliable Real-Time Optimization of Nonconvex Systems Described by Parametrized Partial Differential Equations
Name
HPCES020.pdf
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326.88 KB
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Adobe PDF
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59dbaf19b40f87ae947a84dfb1890992
Author(s)
Oliveira, I.B.
Patera, Anthony T.
Date Issued
January 2003
Series/Report no.
High Performance Computation for Engineered Systems (HPCES);
Abstract
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.
Subjects
parametrized partial differential equations
reduced-basis
computational decomposition
a posteriori error bounds
Interior Point Methods
Sequential Quadratic Programming
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