Optimization Algorithms on Matrix Manifolds
- P. Absil, R. Mahony, R. Sepulchre
- Computer Science
- 23 December 2007
Optimization Algorithms on Matrix Manifolds offers techniques with broad applications in linear algebra, signal processing, data mining, computer vision, and statistical analysis and will be of interest to applied mathematicians, engineers, and computer scientists.
Manopt, a matlab toolbox for optimization on manifolds
- Nicolas Boumal, Bamdev Mishra, P. Absil, R. Sepulchre
- Computer ScienceJournal of machine learning research
- 23 August 2013
The Manopt toolbox, available at www.manopt.org, is a user-friendly, documented piece of software dedicated to simplify experimenting with state of the art Riemannian optimization algorithms, which aims particularly at lowering the entrance barrier.
Constructive Nonlinear Control
- R. Sepulchre, M. Jankovic, P. Kokotovic
- Mathematics
- 27 September 2011
1 Introduction -- 1.1 Passivity, Optimality, and Stability -- 1.2 Feedback Passivation -- 1.3 Cascade Designs -- 1.4 Lyapunov Constructions -- 1.5 Recursive Designs -- 1.6 Book Style and Notation --…
Generalized Power Method for Sparse Principal Component Analysis
- M. Journée, Y. Nesterov, Peter Richtárik, R. Sepulchre
- Computer ScienceJournal of machine learning research
- 28 November 2008
A new approach to sparse principal component analysis (sparse PCA) aimed at extracting a single sparse dominant principal component of a data matrix, or more components at once, respectively is developed.
Stabilization of Planar Collective Motion: All-to-All Communication
- R. Sepulchre, D. Paley, Naomi Ehrich Leonard
- MathematicsIEEE Transactions on Automatic Control
- 15 May 2007
The results of the paper provide a low-order parametric family of stabilizable collectives that offer a set of primitives for the design of higher-level tasks at the group level.
Synchronization in networks of identical linear systems
- L. Scardovi, R. Sepulchre
- MathematicsIEEE Conference on Decision and Control
- 22 May 2008
An internal model principle is necessary and sufficient for linear output synchronization
- P. Wieland, R. Sepulchre, F. Allgöwer
- Mathematicsat - Automatisierungstechnik
- 1 May 2011
A Differential Lyapunov Framework for Contraction Analysis
- F. Forni, R. Sepulchre
- MathematicsIEEE Transactions on Automatic Control
- 14 August 2012
The paper provides an analog theorem for incremental stability analysis by lifting the Lyapunov function to the tangent bundle and endows the state-space with a Finsler structure.
Collective Motion, Sensor Networks, and Ocean Sampling
- Naomi Ehrich Leonard, D. Paley, F. Lekien, R. Sepulchre, D. Fratantoni, R. Davis
- MathematicsProceedings of the IEEE
- 5 March 2007
This paper addresses the design of mobile sensor networks for optimal data collection by using a performance metric, used to derive optimal paths for the network of mobile sensors, to define the optimal data set.
Riemannian Geometry of Grassmann Manifolds with a View on Algorithmic Computation
- P. Absil, R. Mahony, R. Sepulchre
- Mathematics
- 2004
We give simple formulas for the canonical metric, gradient, Lie derivative, Riemannian connection, parallel translation, geodesics and distance on the Grassmann manifold of p-planes in Rn. In these…
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