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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| Published in | IEEE transactions on signal processing Vol. 50; no. 3; pp. 635 - 650 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
New York, NY
IEEE
01.03.2002
Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1053-587X 1941-0476 |
| DOI | 10.1109/78.984753 |
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| 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. |
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| AbstractList | 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. 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 |
| Author | Manton, J.H. |
| Author_xml | – sequence: 1 givenname: J.H. surname: Manton fullname: Manton, J.H. organization: Dept. of Electr. & Electron. Eng., Melbourne Univ., Parkville, Vic., Australia |
| BackLink | http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=13499101$$DView record in Pascal Francis |
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| Snippet | 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... 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... |
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| SubjectTerms | 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 |
| Title | Optimization algorithms exploiting unitary constraints |
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