Spectral finite-element methods for parametric constrained optimization problems.

Journal Article · Thu Jan 01 04:00:00 EST 2009 · SIAM J. Numer. Anal.

DOI:https://doi.org/10.1137/060676374· OSTI ID:962061

Anitescu, M

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.

• Research Organization: Argonne National Laboratory (ANL)
• Sponsoring Organization: SC
• DOE Contract Number: AC02-06CH11357
• OSTI ID: 962061
• Report Number(s): ANL/MCS/JA-61279
• Journal Information: SIAM J. Numer. Anal., Journal Name: SIAM J. Numer. Anal. Journal Issue: 3 ; 2009 Vol. 47
• Country of Publication: United States
• Language: ENGLISH

Related Subjects

97 MATHEMATICS AND COMPUTING
99 GENERAL AND MISCELLANEOUS
APPROXIMATIONS
EIGENVALUES
FINITE ELEMENT METHOD
OPTIMIZATION
POLYNOMIALS
ROUGHNESS