P.-A. Absil

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Chargé de cours (Associate Professor)
Département d'ingénierie mathématique
Université catholique de Louvain

Publications, software, selected talks, and a picture are available.

Contact information

Research groups

Biography

Teaching

• INMA1170: Numerical Analysis
• INMA1375: Project in Applied Mathematics
• INMA2360: Advanced Methods in Automatic Control
• INMA2361: Nonlinear Systems

Education

• PhD in Engineering (``doctorat en sciences appliquées''), University of Liege, February 2003.
  Thesis: Invariant Subspace Computation: A Geometric Approach. Advisor: Prof. R. Sepulchre.
• Engineering degree in physics, University of Liege, 1998.
  Diploma thesis: Nonlinear analysis of cardiological signals towards clinical applications. Supervisor: Prof. R. Sepulchre.

Research Areas

• Numerics on manifolds: Applications to numerical linear algebra
• Numerical optimization: Mathematical programming; Optimization on manifolds
• Dynamical systems: Dynamical systems that solve computational problems
• Automatic control: Swing-up and balancing strategies for the Pendubot
• Biological data analysis: Cardiac rhythm variability; Sleep apnea detection; Gene expression analysis

Selected Talks

• Slides of the BFG'09 talk "Optimization on manifolds: methods and applications", Leuven, 18 Sep 2009
• Slides of the Stiefel Centennial Lecture, Zurich, 10 Sep 2009
• The following links give access to paper ID sheets from which slides are accessible:
  • Vector transport on manifolds (ICIAM talk)
  • Optimization on manifolds (DYSCO meeting talk)
  • Model-based methods for computing extreme eigenpairs of definite pencils
  • Trust-region methods on Riemannian manifolds

Publications

Book

Optimization Algorithms on Matrix Manifolds P.-A. Absil, R. Mahony, R. Sepulchre Princeton University Press, 2008

Full papers (journal articles, technical reports, chapters in books)

On the best low multilinear rank approximation of higher-order tensors


Mariya Ishteva, P.-A. Absil, Sabine Van Huffel, Lieven De Lathauwer
Technical report ESAT-SISTA-10-10 and UCL-INMA-2010.006


Two-sided Grassmann-Rayleigh quotient iteration


P.-A. Absil, P. Van Dooren
Technical report UCL-INMA-2007.024
Numerische Mathematik, 114(4), pp. 549-571, February 2010

The Information Inequality for Function Spaces: A tight lower bound on the Autocovariance


Tzvetan Ivanov, Brian D.O. Anderson, P.-A. Absil, Michel Gevers
Technical report UCL-INMA-2009.137

Riemannian BFGS algorithm with applications


Chunhong Qi, Kyle A. Gallivan, P.-A. Absil
Technical report UCL-INMA-2009.062

Optimization on manifolds: methods and applications


P.-A. Absil
Technical report UCL-INMA-2009.043

Identification method for time-varying ARX models


Quentin Rentmeesters, P.-A. Absil, Paul Van Dooren
Technical report UCL-INMA-2009.067
Submitted.

On Tight Upper Bounds on the Supremum Norm using Norms induced by Inner Products


Tzvetan Ivanov, Brian D. O. Anderson, P.-A. Absil, Michel Gevers
Technical report UCL-INMA-2009.028

Best low multilinear rank approximation of higher-order tensors, based on the Riemannian trust-region scheme


Mariya Ishteva, Lieven De Lathauwer, P.-A. Absil, Sabine Van Huffel
Technical report ESAT-SISTA-09-142
Technical report UCL-INMA-2009.026

All roads lead to Newton: Feasible second-order methods for equality-constrained optimization


P.-A. Absil, Jochen Trumpf, Robert Mahony, Ben Andrews
Technical report UCL-INMA-2009.024

A gradient-descent method for curve fitting on Riemannian manifolds


Chafik Samir, P.-A. Absil, Anuj Srivastava, Eric Klassen
Technical report UCL-INMA-2009.023

Differential-geometric Newton method for the best rank-(R1,R2,R3) approximation of tensors


Mariya Ishteva, Lieven De Lathauwer, P.-A. Absil, Sabine Van Huffel
Technical report UCL-INMA-2008.074
Internal Report 08-111, ESAT-SISTA, K.U.Leuven (Leuven, Belgium), 2008.
doi:10.1007/s11075-008-9251-2
Numerical Algorithms, 51(2), pp. 179-194, June 2009.

A geometric Newton method for Oja's vector field


P.-A. Absil, M. Ishteva, L. De Lathauwer, S. Van Huffel
Technical report UCL-INMA-2008.013
Neural Computation, 21(5), pp. 1415-1433, May 2009.

Accelerated line-search and trust-region methods


P.-A. Absil, K. A. Gallivan
Technical report UCL-INMA-2008.011
SIAM Journal on Numerical Analysis, 47(2), pp. 997-1018, February 2009.

H2-optimal approximation of MIMO linear dynamical systems


Paul Van Dooren, Kyle A. Gallivan, P.-A. Absil
Technical report UCL-INMA-2008.126.

Low-rank optimization for semidefinite convex problems


M. Journée, F. Bach, P.-A. Absil, R. Sepulchre
Technical report UCL-INMA-2008.127
Submitted.

Numerical representations of a universal subspace flow for linear programs


P.-A. Absil
Technical report UCL-INMA-2008.030
Communications in Information and Systems, 8(2), pp. 71-84, 2008.

An implicit trust-region method on Riemannian manifolds


C. G. Baker, P.-A. Absil, K. A. Gallivan
Technical report UCL-INMA-2007.040
IMA Journal of Numerical Analysis, 28(4), pp. 665-689, October 2008.

Comparing two matrices by means of isometric projections


T. Cason, P.-A. Absil, P. Van Dooren
Technical report UCL-INMA-2008.068
Accepted for publication in the NLASSC-2007 edited volume, Lecture Notes in Electrical Engineering, 2008.

H2-optimal model reduction of MIMO systems


P. Van Dooren, K. A. Gallivan, P.-A. Absil
Technical report UCL-INMA-2007.034
Applied Mathematics Letters, 21(12), pp. 1267-1273, December 2008.

Continuous-time subspace flows related to the symmetric eigenvalue problem


P.-A. Absil, R. Sepulchre, R. Mahony
Technical report UCL-INMA-2007.032
Pacific Journal of Optimization, 4(2), pp. 179-194, May 2008.

Dimensionality reduction for higher-order tensors: algorithms and applications


M. Ishteva, L. De Lathauwer, P.-A. Absil, S. Van Huffel
Technical report UCL-INMA-2007.059
Technical report ESAT-SISTA-07-187
International Journal of Pure and Applied Mathematics, 42(3), pp. 337-343, 2008.

Geometric optimization methods for the analysis of gene expression data


M. Journée, A. E. Teschendorff, P.-A. Absil, S. Tavaré, R. Sepulchre
Principal Manifolds for Data Visualization and Dimension Reduction
Gorban, A.N.; Kégl, B.; Wunsch, D.C.; Zinovyev, A. (Eds.)
Lecture Notes in Computational Science and Engineering, Springer, Volume 58, pp. 271-292, October 2007.

Elucidating the Altered Transcriptional Programs in Breast Cancer using Independent Component Analysis


Andrew E. Teschendorff, Michel Journée, Pierre A. Absil, Rodolphe Sepulchre, Carlos Caldas
PLoS Comput Biol 3(8): e161, August 2007.

Trust-region methods on Riemannian manifolds


P.-A. Absil, C. G. Baker, K. A. Gallivan
Technical report UCL-INMA-2005.132
Foundations of Computational Mathematics, 7(3), pp. 303-330, July 2007.


Newton-KKT interior-point methods for indefinite quadratic programming


P.-A. Absil, A. L. Tits
Technical report UCL-INMA-2005.134
Computational Optimization and Applications, 36(1), pp. 5-41, January 2007.

Continuous-time systems that solve computational problems


P.-A. Absil
International Journal of Unconventional Computing, 2(4), 291-304, 2006.

On the stable equilibrium points of gradient systems


P.-A. Absil, K. Kurdyka
Systems & Control Letters, 55(7), pp. 573-577, July 2006.


A truncated-CG style method for symmetric generalized eigenvalue problems


P.-A. Absil, C. G. Baker, K. A. Gallivan
Journal of Computational and Applied Mathematics, 189(1-2), pp. 274-285, 1 May 2006.


Constraint reduction for linear programs with many inequality constraints


A. L. Tits, P.-A. Absil, W. P. Woessner
SIAM Journal on Optimization, 17(1), pp. 119-146, 21 April 2006.


On the largest principal angle between random subspaces


P.-A. Absil, A. Edelman, P. Koev
Linear algebra and its applications, 414(1), pp. 288-294, 1 April 2006.

Convergence of the Iterates of Descent Methods for Analytic Cost Functions


P.-A. Absil, R. Mahony, B. Andrews
SIAM Journal on Optimization, 16(2), pp. 531-547, 30 December 2005.

Well-posedness and regularity properties of the Grassmann-Rayleigh quotient iteration


P.-A. Absil, U. Helmke, K. Hüper
Technical Report FSU-CSIT-04-26, 9 December 2004.

Cubically convergent iterations for invariant subspace computation


P.-A. Absil, R. Sepulchre, P. Van Dooren, R. Mahony
SIAM J. Matrix Analysis, 26(1), pp. 70-96, 2004.


Continuous dynamical systems that realize discrete optimization on the hypercube


P.-A. Absil, R. Sepulchre
Systems & Control Letters, 52(3-4), pp. 297-304, July 2004.

Riemannian geometry of Grassmann manifolds with a view on algorithmic computation


P.-A. Absil, R. Mahony, R. Sepulchre
Acta Applicandae Mathematicae, 80(2), pp. 199-220, January 2004.

The continuous-time Rayleigh quotient flow on the sphere


R. Mahony, P.-A. Absil
Linear Algebra and its Applications, 368C, pp. 343-357, 2003.

A Grassmann-Rayleigh quotient iteration for computing invariant subspaces


P.-A. Absil, R. Mahony, R. Sepulchre, P. Van Dooren
SIAM Review, 44(1), pp. 57-73, 2002.

Nonlinear analysis of cardiological signals towards clinical applications


P.-A. Absil
Journal A, 41(4), pp. 14-16, 2000.

Nonlinear analysis of cardiac rhythm fluctuations using DFA method


P.-A. Absil, R. Sepulchre, A. Bilge, P. Gérard
Physica A: Statistical Mechanics and its Applications, 272(1-2), pp. 235-244, 1999.

Conference papers

1. Fast Oriented Bounding Box Computation Using Particle Swarm Optimization
   Pierre B. Borckmans, P.-A. Absil
   Technical report UCL-INMA-2009.082
   Accepted for publication in the proceedings of the 18th European Symposium on Artificial Neural Networks (ESANN), 2010
2. An efficient particle filtering technique on the Grassmann manifold
   Quentin Rentmeesters, P.-A. Absil, Paul Van Dooren, Kyle Gallivan, Anuj Srivastava
   Proceedings of the 35th International Conference on Acoustics, Speech, and Signal Processing (ICASSP), to appear
3. Elastic morphing of 2D and 3D objects on a shape manifold
   C. Samir, P. Van Dooren, D. Laurent, K. A. Gallivan, P.-A. Absil
   Technical report UCL-INMA-2008.228
   Lecture Notes in Computer Science, Volume 5627/2009, pp. 563-572, 2009
   doi:10.1007/978-3-642-02611-9
4. Iterative Methods for Low Rank Approximation of Graph Similarity Matrices
   T. P. Cason, P.-A. Absil, P. Van Dooren
   7th International Workshop on Mining and Learning with Graphs, Leuven, Belgium, July 2-4, 2009
5. Fitting Curves on Riemannian Manifolds Using Energy Minimization
   Chafik Samir, P.-A. Absil, Anuj Srivastava, Eric Klassen
   Technical report UCL-INMA-2009.025
   MVA2009 IAPR Conference on Machine Vision Applications, May 20-22, 2009, Yokohama, Japan
   See full paper
6. Embedded geometry of the set of symmetric positive semidefinite matrices of fixed rank
   Bart Vandereycken, P.-A. Absil, Stefan Vandewalle
   Technical report UCL-INMA-2009.014
   Proceeding of the 15th Workshop on Statistical Signal Processing (SSP '09), pp. 389-392, 2009
   doi:10.1109/SSP.2009.5278558
   Preprint available from Bart Vandereycken's home page
7. Gene expression data analysis using spatiotemporal blind source separation
   Matthieu Sainlez, P.-A. Absil, Andrew E. Teschendorff
   Technical report UCL-INMA-2008.171
   Proceedings of the 17th European Symposium on Artificial Neural Networks (ESANN), pp. 159-164, 2009.
8. Soft dimension reduction for ICA by joint diagonalization on the Stiefel manifold
   Fabian J. Theis, Thomas P. Cason, P.-A. Absil
   Technical report UCL-INMA-2008.155
   Lecture Notes in Computer Science, 5441, pp. 354-361, 2009.
9. Using H2 norm to bound H-infinity norm from above on Real Rational Modules
   Tzvetan Ivanov, Brian D. O. Anderson, P.-A. Absil, Michel Gevers
   Technical report UCL-INMA-2009.031
   Proceedings of the European Control Conference 2009, pp. 2259-2264, 2009.
10. The best rank-(R1,R2,R3) approximation of tensors by means of a geometric Newton method
    Mariya Ishteva, Lieven De Lathauwer, P.-A. Absil, Sabine Van Huffel
    Technical report UCL-INMA-2008.075
    Internal Report 08-115, ESAT-SISTA, K.U.Leuven (Leuven, Belgium), 2008
    Proceedings of Sixth (6th) International Conference of Numerical Analysis and Applied Mathematics (ICNAAM 2008).
    
11. Application of real rational modules in system identification
    T. Ivanov, P.-A. Absil, B. D. O. Anderson, M. Gevers
    Technical report UCL-INMA-2008.026
    Proceedings of the 47th IEEE Conference on Decision and Control (CDC 2008), pp. 111-116, 2008
12. Design of continuous-time flows on intertwined orbit spaces
    P.-A. Absil, C. Lageman, J. H. Manton
    Proceedings of the 46th IEEE Conference on Decision and Control (CDC 2007), pp. 6244-6249, 2007.
13. Gradient-Optimization on the Orthogonal Group for Independent Component Analysis
    Michel Journée, Pierre-Antoine Absil, Rodolphe Sepulchre
    Technical report UCL-INMA-2007.058
    Independent Component Analysis and Signal Separation
    7th International Conference, ICA 2007, London, UK, September 9-12, 2007. Proceedings
    Lecture Notes in Computer Science, 4666, pp. 57-64, 2007.
14. Geometric optimization methods for independent component analysis applied on gene expression data
    M. Journée, A. E. Teschendorff, P.-A. Absil, R. Sepulchre
    Technical report UCL-INMA-2008.076
    Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing, 2007 (ICASSP 2007), pp. IV 1413-1416, 2007
    doi:10.1109/ICASSP.2007.367344
15. An implicit Riemannian trust-region method for the symmetric generalized eigenproblem
    C. G. Baker, P.-A. Absil, K. A. Gallivan
    Computational Science -- ICCS 2006
    6th International Conference, Reading, UK, May 28-31, 2006, Proceedings, Part I
    Lecture Notes in Computer Science, 3991, 29 April 2006.
16. Joint diagonalization on the oblique manifold for independent component analysis
    P.-A. Absil, K. A. Gallivan
    Proceedings of the 2006 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2006), May 2006. doi:10.1109/ICASSP.2006.1661433
17. Adaptive model trust region methods for generalized eigenvalue problems
    P.-A. Absil, C. G. Baker, K. A. Gallivan
    Computational Science -- ICCS 2005
    5th International Conference, Atlanta, GA, USA, May 22-25, 2005. Proceedings, Part I
    Lecture Notes in Computer Science, 3514, 20 April 2005.
    
18. Trust-region methods on Riemannian manifolds with applications in numerical linear algebra
    P.-A. Absil, C. G. Baker, K. A. Gallivan
    Proceedings of the Sixteenth International Symposium on Mathematical Theory of Networks and Systems (MTNS), Katholieke Universiteit Leuven, Belgium (2004).
19. Continuous-time flows on quotient spaces for principal component analysis
    P.-A. Absil
    Proceedings of the Sixteenth International Symposium on Mathematical Theory of Networks and Systems (MTNS), Katholieke Universiteit Leuven, Belgium (2004).
20. Generalized shifted inverse iterations on Grassmann manifolds
    J. Jordan, P.-A. Absil, R. Sepulchre
    Proceedings of the Sixteenth International Symposium on Mathematical Theory of Networks and Systems (MTNS), Katholieke Universiteit Leuven, Belgium (2004).
21. A Newton algorithm for invariant subspace computation with large basins of attraction
    P.-A. Absil, R. Sepulchre, P. Van Dooren and R. Mahony
    Proceedings of the 42nd IEEE Conference on Decision and Control, December 9-12, 2003, Hyatt Regency Maui, Hawaii, USA, pp. 2352-2357, December 2003.
22. The continuous-time Rayleigh quotient flow on the Grassmann manifold
    P.-A. Absil, R. Mahony, R. Sepulchre.
    Proceedings of MTNS, University of Notre Dame, August 12-16 (2002)
23. A Grassmann-Rayleigh quotient iteration for computing invariant subspaces
    P.-A. Absil, R. Mahony, R. Sepulchre, P. Van Dooren
    Proceedings of the 39th IEEE Conference on Decision and Control (CDC), Sydney (2000).
24. A hybrid control scheme for swing-up acrobatics
    P.-A. Absil, R. Sepulchre.
    Proceedings of the European Conference on Control ECC 2001, Porto, Portugal, September 4-7 (2001).
25. Sleep apnea syndrome diagnosis by analysis of the cardiac interbeat RR time series
    P.-A. Absil, R. Sepulchre, A. Bilge, P. Gérard.
    Proceedings of the International Workshop on Advanced Black-Box Techniques for Nonlinear Modeling, Katholieke Universiteit Leuven, Belgium (1998).

Selected abstracts

1. Review of Similarity Matrices and Application to Subgraph Matching
   T. P. Cason, P.-A. Absil, P. Van Dooren
   Submitted
2. Image segmentation and real-time video tracking using graph based techniques
   Arnaud Browet, Paul Van Dooren, P.-A. Absil
   Submitted
3. The Information Inequality on Function Spaces
   Tzvetan Ivanov, Michel Gevers, P.-A. Absil, Brian D.O. Anderson
   Submitted
4. Fast Oriented Bounding Box Computation Using Particle Swarm Optimization
   P. Borckmans, P.-A. Absil
   Submitted
5. Fitting smooth curves on a Riemannian manifold
   C. Samir, P.-A. Absil, A. Srivastava, E. Klassen
   Technical report UCL-INMA-2009.083
   J. De Schutter, M. Diehl, F. Glineur, E. Jarlebring, Q. Louveaux, W. Michiels, I. Smets, J. Suykens, J. Swevers, J. Vandewalle, J. Van Impe, M. Verschuure (eds.), Book of Abstracts of the 14th Belgian-French-German Conference on Optimization (BFG'09), Leuven, ISBN 9789073802001, 2009, p 55
6. The Riemannian BFGS algorithm with applications
   Chunhong Qi, K. A. Gallivan, P.-A. Absil
   Technical report UCL-INMA-2009.084
   BFG'09, p 57
7. Optimization on low-rank positive semidefinite matrices
   M. Journée, F. Bach, P.-A. Absil, R. Sepulchre
   Technical report UCL-INMA-2009.085
   BFG'09, p 71
8. Identification method for time-varying ARX models
   Q. Rentmeesters, P.-A. Absil, P. Van Dooren
   Technical report UCL-INMA-2009.086
   BFG'09, p 114

Software

• GenRTR (by Chris Baker, Pierre-Antoine Absil, and Kyle Gallivan): the Generic Riemannian Trust-Region package. GenRTR is a MATLAB package for the optimization of functions defined on Riemannian manifolds.