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SPECTRAL FINITE-ELEMENT METHODS FOR PARAMETRIC CONSTRAINED OPTIMIZATION PROBLEMS.
- Source :
-
SIAM Journal on Numerical Analysis . 2009, Vol. 47 Issue 4, p1739-1759. 21p. 2 Graphs. - Publication Year :
- 2009
-
Abstract
- We present a method to approximate the solution mapping of parametric constrained optimization problems. The approximation, which is of the spectral finite element type, is represented as a linear combination of orthogonal polynomials. Its coefficients are determined by solving an appropriate finite-dimensional constrained optimization problem. We show that, under certain conditions, the latter problem is solvable because it is feasible for a sufficiently large degree of the polynomial approximation and has an objective function with bounded level sets. In addition, the solutions of the finite-dimensional problems converge for an increasing degree of the polynomials considered, provided that the solutions exhibit a sufficiently large and uniform degree of smoothness. Our approach solves, in the case of optimization problems with uncertain parameters, the most computationally intensive part of stochastic finite-element approaches. We demonstrate that our framework is applicable to parametric eigenvalue problems. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00361429
- Volume :
- 47
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- SIAM Journal on Numerical Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 51789548
- Full Text :
- https://doi.org/10.1137/060676374