Optimization algorithms exploiting unitary constraints

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 optimiza...

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Vydáno v:IEEE transactions on signal processing Ročník 50; číslo 3; s. 635 - 650
Hlavní autor: Manton, J.H.
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York, NY IEEE 01.03.2002
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:
Algorithms
Applied sciences
Constraint optimization
Cost function
Eigenvalues
Eigenvalues and eigenfunctions
Eigenvectors
Exact sciences and technology
Frequency estimation
Information, signal and communications theory
Iterative algorithms
Manifolds
Mathematical analysis
Mathematical methods
Norms
Operational research and scientific management
Operational research. Management science
Optimization
Optimization. Search problems
Signal processing
Signal processing algorithms
Space technology
Subspace constraints
Symmetric matrices
Telecommunications and information theory
Performance evaluation
Simulation
Steepest descent method
Convergence rate
Signal processing
Eigenvalue problem
Algorithm
Newton method
Constrained optimization
ISSN:1053-587X, 1941-0476
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Popis
Shrnutí: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.
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ISSN:1053-587X
1941-0476
DOI:10.1109/78.984753