Solving linear partial differential equations via semidefinite optimization
Name
48995201-MIT.pdf
Description
Full printable version
Size
1.38 MB
Format
Adobe PDF
Checksum (MD5)
751dbf5f656524eea321bf62fcf18ae9
Author(s)
Caramanis, Constantine (Constantine Michael), 1977-
Advisor(s)
Dimitris Bertsimas.
Date Issued
2001
Publisher
Massachusetts Institute of Technology
Abstract
Using recent progress on moment problems, and their connections with semidefinite optimization, we present in this thesis a new methodology based on semidefinite optimization, to obtain a hierarchy of upper and lower bounds on both linear and nonlinear functionals defined on solutions of linear partial differential equations. We apply the proposed methods to examples of PDEs in one and two dimensions with very encouraging results. We also provide computational evidence that the semidefinite constraints are critically important in improving the quality of the bounds, that is without them the bounds are weak.
Description
Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2001.
Includes bibliographical references (p. 49-51).
Subjects
Electrical Engineering and Computer Science.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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