Recent advances in optimization and its applications in engineering

548 Pages·2010·8.442 MB·English

by  Diehl M (ed.)

Recent Advances in Optimization and its
Applications in Engineering

· · ·
Moritz Diehl Franc¸ois Glineur Elias Jarlebring
Wim Michiels
Editors
Recent Advances in
Optimization and its
Applications in Engineering
123
Editors
Prof.Dr.MoritzDiehl Prof.Dr.Franc¸oisGlineur
KatholiekeUniversiteitLeuven CORE-UCL
Dept.ElectricalEngineering(ESAT) VoieduRomanPays34
andOptimizationinEngineering 1348Louvain-la-Neuve
Center(OPTEC) Belgium
KasteelparkArenberg10 [email protected]
3001Leuven
Belgium
[email protected]
Dr.EliasJarlebring Prof.Dr.WimMichiels
KatholiekeUniversiteitLeuven KatholiekeUniversiteitLeuven
DepartmentComputerwetenschappen DepartmentComputerwetenschappen
andOptimizationinEngineering andOptimizationinEngineering
Center(OPTEC) Center(OPTEC)
Celestijnenlaan200A Celestijnenlaan200A
3001Heverlee 3001Heverlee
Belgium Belgium
[email protected] [email protected]
ISBN978-3-642-12597-3 e-ISBN978-3-642-12598-0
DOI10.1007/978-3-642-12598-0
SpringerHeidelbergDordrechtLondonNewYork
LibraryofCongressControlNumber:2010933976
(cid:2)c Springer-VerlagBerlinHeidelberg2010
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Preface
The field of mathematical optimization combines a rich body of fundamen-
tal theory with a powerful collection of computational methods and a variety
of exciting applications. The field evolves fast, and the last decade has been
characterized by major developments in optimization theory, improvements
in numerical methods also benefiting from the parallel developments in com-
putational hardware, and emergence of novel applications.
Many of these novel applications belong to engineering, as globalization
of the economy, increased competition, limited natural resources and ever
stronger environmental constraints call for better performance of industrial
products and higher productivity of production processes. This new environ-
ment poses real challenges to engineering research, design and development.
Adequatetranslationoftheconflictingobjectivesintooptimizationproblems,
availability of efficient and reliable numerical algorithms and correct inter-
pretation of the results are essential in addressing these challenges. We are
convinced that significant advances can be achieved by cross-fertilization and
integrationoftherecentdevelopmentsinthemathematicaloptimizationcom-
munity on the one hand and the different engineering communities on the
other hand.
The present volume contains a careful selection of articles on recent ad-
vances in optimization theory, numerical methods, and their applications in
engineering.Theauthorsmetatthe14thBelgian-French-GermanConference
on Optimization (BFG09) that took place in Leuven in September 14–18,
2009. Theconference wasorganizedbythe Optimization inEngineering Cen-
ter OPTEC at the Katholieke Universiteit Leuven (K.U.Leuven), in collab-
oration with the Center for Operations Research and Econometrics (CORE)
at the Universit´e Catholique de Louvain (UCLouvain).
Inthecontextsketchedabove,BFG09’sspecialtopicwas“Optimizationin
Engineering”,aimingatdeepeningthecontactsbetweenengineeringoptimiz-
ers and mathematical optimizers. We believe that this aim has been reached
and that it is well reflected in the present volume, which is divided into the
followingchapters:convexoptimization,nonlinearoptimization,optimization
VI Preface
onmanifolds,optimalcontrol,modelpredictivecontrol,PDE-constrainedop-
timization and engineering applications of optimization. We want in particu-
lar to point out the overview articles by three of the invited speakers at the
BFG09 (M. Du¨r, P.-A. Absil, J.-B. Caillau) as well as by the winners of the
best talk and best poster prizes (A. Potschka, M. Ishteva). These overview
articles can be found at the beginning of their respective chapters.
This book would not have been possible without the substantial help of
many anonymous reviewers whom we want to thank at this place. Accep-
tance decisions for each submitted article were based on at least two reviews,
whichalsohelpedtheauthorstofurtherimprovetheircontributions.Wealso
gratefully acknowledge financial support by the Fonds Wetenschappelijk On-
derzoek – Vlaanderen (FWO) and the Fonds de la Recherche Scientifique
(F.R.S.-FNRS).
We are particularly indebted to Jacqueline De bruyn and Ioanna Stamati
forthenumeroushoursspentcommunicatingwiththeauthorsofthisvolume
on technical questions, and in particular to Ioanna Stamati for compiling
the final LATEX manuscript. Last but not least, we want to thank the staff at
Springer,inparticularBirgitKollmar-ThoniandEvaHestermann-Beyerle,for
their efficient and professional support, including the design of an innovative
cover, which features a word cloud (obtained from the web site wordle.net)
reflecting importance of the most frequent terms used throughout the book.
Wewishallreadersofthisbookthesamepleasurewehadincompilingit!
Leuven and Louvain-La-Neuve, Moritz Diehl
Belgium, July 2010 Fran¸cois Glineur
Elias Jarlebring
Wim Michiels
Contents
Part I Convex Optimization
Copositive Programming – a Survey
Mirjam Du¨r::::::::::::::::::::::::::::::::::::::::::::::::::::: 3
A Robust H∞ Quasi-LPV Approach for Designing Nonlinear
Observers
Daniel F. Coutinho, Alain Vande Wouwer :::::::::::::::::::::::::: 21
Solving Infinite-dimensional Optimization Problems by
Polynomial Approximation
Olivier Devolder, Fran¸cois Glineur, Yurii Nesterov ::::::::::::::::::: 31
Abstract Cones of Positive Polynomials and Their Sums of
Squares Relaxations
Roland Hildebrand ::::::::::::::::::::::::::::::::::::::::::::::: 41
Asynchronous Gossip Algorithm for Stochastic Optimization:
Constant Stepsize Analysis
S. Sundhar Ram, Angelia Nedi´c, Venu V. Veeravalli:::::::::::::::::: 51
Part II Nonlinear Optimization
On Hessian- and Jacobian-Free SQP Methods - a Total
Quasi-Newton Scheme with Compact Storage
Torsten Bosse, Andreas Griewank, Lutz Lehmann, and Volker
Schloßhauer ::::::::::::::::::::::::::::::::::::::::::::::::::::: 63
Approximate Geometric Ellipsoid Fitting: A CG-Approach
Martin Kleinsteuber, Knut Hu¨per :::::::::::::::::::::::::::::::::: 73
VIII Contents
Continuous Reformulation of MINLP Problems
Korbinian Kraemer and Wolfgang Marquardt :::::::::::::::::::::::: 83
Local Convergence of Sequential Convex Programming for
Nonconvex Optimization
Quoc Tran Dinh, Moritz Diehl::::::::::::::::::::::::::::::::::::: 93
Fixed-Order H-infinity Optimization of Time-Delay Systems
Suat Gumussoy, Wim Michiels ::::::::::::::::::::::::::::::::::::103
UsingModelOrderReductionfortheParameterOptimization
of Large Scale Dynamical Systems
Yao Yue, Karl Meerbergen ::::::::::::::::::::::::::::::::::::::::113
Part III Optimization on Manifolds
Optimization On Manifolds: Methods and Applications
P.-A. Absil, R. Mahony, R. Sepulchre ::::::::::::::::::::::::::::::125
On the Best Low Multilinear Rank Approximation of
Higher-order Tensors
Mariya Ishteva, P.-A. Absil, Sabine Van Huffel, Lieven De Lathauwer ::145
Refining Sparse Principal Components
M. Journ´ee, F. Bach, P.-A. Absil, R. Sepulchre::::::::::::::::::::::165
Optimal Data Fitting on Lie Groups: a Coset Approach
C. Lageman, R. Sepulchre:::::::::::::::::::::::::::::::::::::::::173
Riemannian BFGS Algorithm with Applications
Chunhong Qi, Kyle A. Gallivan, P.-A. Absil:::::::::::::::::::::::::183
Identification Method for Time-Varying ARX Models
Quentin Rentmeesters, P.-A. Absil, Paul Van Dooren ::::::::::::::::193
Part IV Optimal Control
On Some Riemannian Aspects of Two and Three-Body
Controlled Problems
J.-B. Caillau, B. Daoud, J. Gergaud :::::::::::::::::::::::::::::::205
Optimization techniques for the computation of the effective
Hamiltonian
Maurizio Falcone and Marco Rorro:::::::::::::::::::::::::::::::::225