Optimization algorithms exploiting unitary constraints
Top Cited Papers
- 7 August 2002
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Signal Processing
- Vol. 50 (3), 635-650
- https://doi.org/10.1109/78.984753
Abstract
This paper presents novel algorithms that iteratively converge to a local minimum of a real-valued function f (X) subject to the constraint that the columns of the complex-valued matrix X are mutually orthogonal and have unit norm. The algorithms are derived by reformulating the constrained optimization problem as an unconstrained one on a suitable manifold. This significantly reduces the dimensionality of the optimization problem. Pertinent features of the proposed framework are illustrated by using the framework to derive an algorithm for computing the eigenvector associated with either the largest or the smallest eigenvalue of a Hermitian matrix.Keywords
This publication has 27 references indexed in Scilit:
- An adaptive quasi-Newton algorithm for eigensubspace estimationIEEE Transactions on Signal Processing, 2000
- Algebraic methods for deterministic blind beamformingProceedings of the IEEE, 1998
- Weighted low-rank approximation of general complex matrices and its application in the design of 2-D digital filtersIEEE Transactions on Circuits and Systems I: Regular Papers, 1997
- A least-squares approach to joint diagonalizationIEEE Signal Processing Letters, 1997
- The constrained newton method on a Lie group and the symmetric eigenvalue problemLinear Algebra and its Applications, 1996
- An analytical constant modulus algorithmIEEE Transactions on Signal Processing, 1996
- Convex Functions and Optimization Methods on Riemannian ManifoldsPublished by Springer Nature ,1994
- Indeterminacy and identifiability of blind identificationIEEE Transactions on Circuits and Systems, 1991
- A survey of conjugate gradient algorithms for solution of extreme eigen-problems of a symmetric matrixIEEE Transactions on Acoustics, Speech, and Signal Processing, 1989
- Adaptive eigensubspace algorithms for direction or frequency estimation and trackingIEEE Transactions on Acoustics, Speech, and Signal Processing, 1988