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Reliable Real-Time Optimization of Nonconvex Systems Described by Parametrized Partial Differential Equations

Author(s)
Oliveira, I.B.; Patera, Anthony T.
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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.
Date issued
2003-01
URI
http://hdl.handle.net/1721.1/3707
Series/Report no.
High Performance Computation for Engineered Systems (HPCES);
Keywords
parametrized partial differential equations, reduced-basis, computational decomposition, a posteriori error bounds, Interior Point Methods, Sequential Quadratic Programming

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