Conjugate Gradient Algorithm for Optimization under Unitary Matrix Constraint
In this paper we introduce a Riemannian algorithm for minimizing (or maximizing) a real-valued function J of complex-valued matrix argument W under the constraint that W is an n×n unitary matrix. This type of constrained optimization problem arises in many array and multi-channel signal processing a...
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| Format: | Journal article |
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2015
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| _version_ | 1797073340521775104 |
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| author | Abrudan, T Eriksson, J Koivunen, V |
| author_facet | Abrudan, T Eriksson, J Koivunen, V |
| author_sort | Abrudan, T |
| collection | OXFORD |
| description | In this paper we introduce a Riemannian algorithm for minimizing (or maximizing) a real-valued function J of complex-valued matrix argument W under the constraint that W is an n×n unitary matrix. This type of constrained optimization problem arises in many array and multi-channel signal processing applications. We propose a conjugate gradient (CG) algorithm on the Lie group of unitary matrices U(n). The algorithm fully exploits the group properties in order to reduce the computational cost. Two novel geodesic search methods exploiting the almost periodic nature of the cost function along geodesics on U(n) are introduced. We demonstrate the performance of the proposed CG algorithm in a blind signal separation application. Computer simulations show that the proposed algorithm outperforms other existing algorithms in terms of convergence speed and computational complexity. |
| first_indexed | 2024-03-06T23:20:40Z |
| format | Journal article |
| id | oxford-uuid:689e48e4-76f3-4fd3-8b3b-30752d8ef77d |
| institution | University of Oxford |
| last_indexed | 2024-03-06T23:20:40Z |
| publishDate | 2015 |
| record_format | dspace |
| spelling | oxford-uuid:689e48e4-76f3-4fd3-8b3b-30752d8ef77d2022-03-26T18:45:59ZConjugate Gradient Algorithm for Optimization under Unitary Matrix ConstraintJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:689e48e4-76f3-4fd3-8b3b-30752d8ef77dDepartment of Computer Science2015Abrudan, TEriksson, JKoivunen, VIn this paper we introduce a Riemannian algorithm for minimizing (or maximizing) a real-valued function J of complex-valued matrix argument W under the constraint that W is an n×n unitary matrix. This type of constrained optimization problem arises in many array and multi-channel signal processing applications. We propose a conjugate gradient (CG) algorithm on the Lie group of unitary matrices U(n). The algorithm fully exploits the group properties in order to reduce the computational cost. Two novel geodesic search methods exploiting the almost periodic nature of the cost function along geodesics on U(n) are introduced. We demonstrate the performance of the proposed CG algorithm in a blind signal separation application. Computer simulations show that the proposed algorithm outperforms other existing algorithms in terms of convergence speed and computational complexity. |
| spellingShingle | Abrudan, T Eriksson, J Koivunen, V Conjugate Gradient Algorithm for Optimization under Unitary Matrix Constraint |
| title | Conjugate Gradient Algorithm for Optimization under Unitary Matrix Constraint |
| title_full | Conjugate Gradient Algorithm for Optimization under Unitary Matrix Constraint |
| title_fullStr | Conjugate Gradient Algorithm for Optimization under Unitary Matrix Constraint |
| title_full_unstemmed | Conjugate Gradient Algorithm for Optimization under Unitary Matrix Constraint |
| title_short | Conjugate Gradient Algorithm for Optimization under Unitary Matrix Constraint |
| title_sort | conjugate gradient algorithm for optimization under unitary matrix constraint |
| work_keys_str_mv | AT abrudant conjugategradientalgorithmforoptimizationunderunitarymatrixconstraint AT erikssonj conjugategradientalgorithmforoptimizationunderunitarymatrixconstraint AT koivunenv conjugategradientalgorithmforoptimizationunderunitarymatrixconstraint |