ITEM METADATA RECORD
Title: The Use of Model Order Reduction in Design Optimization Algorithms (Het gebruik van modelreductie in algoritmen voor ontwerpoptimalisatie)
Other Titles: The Use of Model Order Reduction in Design Optimization Algorithms
Authors: Yue, Yao
Issue Date: 6-Nov-2012
Table of Contents: Abstract iii
Abbreviations vii
List of Symbols ix
Contents xiii
List of Figures xvii
List of Tables xix
1 Introduction 1
1.1 Design optimization . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Examples of design optimization . . . . . . . . . . . . . . . . . 3
1.3 Using model order reduction to speed up design optimization . . 11
1.4 Using interpolatory model order reduction for further speedups 13
1.5 Structure of the thesis . . . . . . . . . . . . . . . . . . . . . . . 15

2 Background on numerical optimization 17
2.1 A brief introduction to line search methods and trust region
methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2 An optimization algorithm for design optimization . . . . . . . 23
3 Background on Krylov-Padé type model order reduction 29


3.1 Krylov subspace . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.2 Krylov-Padé type MOR with one parameter . . . . . . . . . . . 33
3.3 Krylov-Padé type MOR with multiple parameters . . . . . . . . 40
3.4 Two-sided PIMTAP . . . . . . . . . . . . . . . . . . . . . . . . 43

4 Combining (P)MOR with optimization 47
4.1 Derivative computations via Krylov-Padé Type MOR/PMOR . 48
4.2 Two frameworks to use MOR/PMOR in accelerating optimization 58
4.3 Improvement of the PMOR Framework for smooth objective
functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

5 Using surrogate models with error estimators in optimization 73
5.1 The relaxed first order condition . . . . . . . . . . . . . . . . . 74
5.2 An error-aware sufficient decrease condition for convergence under 77
the relaxed first order condition . . . . . . . . . . . . . . . . . .
5.3 Two design optimization algorithms based on the relaxed first 87
order condition . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4 Implementation details for ETR and EP . . . . . . . . . . . . . 92

6 Using Interpolatory MOR in optimization 93
6.1 A heuristic error bound . . . . . . . . . . . . . . . . . . . . . . 93
6.2 Combining interpolatory reduced models with ETR and EP . . 97
6.3 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . 99

7 Using block Krylov methods to preserve design parameters for low-rank structures 107
7.1 Block Krylov methods for low-rank parametric structures . . . 107
7.2 Numerical results . . . . . . . . . . . . . . . . . . . . . . . . . . 114

8 Conclusions and future directions 117
8.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
8.2 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
8.3 Future directions . . . . . . . . . . . . . . . . . . . . . . . . . . 120

A Using line search methods in exploiting interpolatory reduced models 123
A.1 Error-aware Armijo conditions and a practical working procedure 123
A.2 Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

Bibliography 129

Curriculum Vitae 143
ISBN: 978-94-6018-591-5
Publication status: published
KU Leuven publication type: TH
Appears in Collections:Numerical Analysis and Applied Mathematics Section

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