Adaptive alternating minimization algorithms
The classical alternating minimization (or projection) algorithm has been successful in the context of solving optimization problems over two variables. The iterative nature and simplicity of the algorithm has led to its application in many areas such as signal processing, information theory, contro...
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| Format: | Article |
| Language: | en_US |
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Institute of Electrical and Electronics Engineers
2010
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| Online Access: | http://hdl.handle.net/1721.1/53588 https://orcid.org/0000-0003-0737-3259 https://orcid.org/0000-0001-9166-4758 |
| _version_ | 1811082477089849344 |
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| author | Niesen, Urs Shah, Devavrat Wornell, Gregory W. |
| author2 | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science |
| author_facet | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Niesen, Urs Shah, Devavrat Wornell, Gregory W. |
| author_sort | Niesen, Urs |
| collection | MIT |
| description | The classical alternating minimization (or projection) algorithm has been successful in the context of solving optimization problems over two variables. The iterative nature and simplicity of the algorithm has led to its application in many areas such as signal processing, information theory, control, and finance. A general set of sufficient conditions for the convergence and correctness of the algorithm are known when the underlying problem parameters are fixed. In many practical situations, however, the underlying problem parameters are changing over time, and the use of an adaptive algorithm is more appropriate. In this paper, we study such an adaptive version of the alternating minimization algorithm. More precisely, we consider the impact of having a slowly time-varying domain over which the minimization takes place. As a main result of this paper, we provide a general set of sufficient conditions for the convergence and correctness of the adaptive algorithm. Perhaps somewhat surprisingly, these conditions seem to be the minimal ones one would expect in such an adaptive setting. We present applications of our results to adaptive decomposition of mixtures, adaptive log-optimal portfolio selection, and adaptive filter design. |
| first_indexed | 2024-09-23T12:04:02Z |
| format | Article |
| id | mit-1721.1/53588 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T12:04:02Z |
| publishDate | 2010 |
| publisher | Institute of Electrical and Electronics Engineers |
| record_format | dspace |
| spelling | mit-1721.1/535882022-10-01T07:54:04Z Adaptive alternating minimization algorithms Niesen, Urs Shah, Devavrat Wornell, Gregory W. Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Wornell, Gregory W. Shah, Devavrat Wornell, Gregory W. Niesen, Urs optimization methods algorithms adaptive signal processing Arimoto–Blahut algorithm Adaptive filters The classical alternating minimization (or projection) algorithm has been successful in the context of solving optimization problems over two variables. The iterative nature and simplicity of the algorithm has led to its application in many areas such as signal processing, information theory, control, and finance. A general set of sufficient conditions for the convergence and correctness of the algorithm are known when the underlying problem parameters are fixed. In many practical situations, however, the underlying problem parameters are changing over time, and the use of an adaptive algorithm is more appropriate. In this paper, we study such an adaptive version of the alternating minimization algorithm. More precisely, we consider the impact of having a slowly time-varying domain over which the minimization takes place. As a main result of this paper, we provide a general set of sufficient conditions for the convergence and correctness of the adaptive algorithm. Perhaps somewhat surprisingly, these conditions seem to be the minimal ones one would expect in such an adaptive setting. We present applications of our results to adaptive decomposition of mixtures, adaptive log-optimal portfolio selection, and adaptive filter design. Hewlett-Packard National Science Foundation (Grant CCF-0515109) 2010-04-08T18:29:18Z 2010-04-08T18:29:18Z 2009-02 2008-09 Article http://purl.org/eprint/type/JournalArticle 0018-9448 http://hdl.handle.net/1721.1/53588 Niesen, U., D. Shah, and G.W. Wornell. “Adaptive Alternating Minimization Algorithms.” Information Theory, IEEE Transactions on 55.3 (2009): 1423-1429. © 2009 IEEE https://orcid.org/0000-0003-0737-3259 https://orcid.org/0000-0001-9166-4758 en_US http://dx.doi.org/10.1109/TIT.2008.2011442 IEEE Transactions on Information Theory Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf Institute of Electrical and Electronics Engineers IEEE |
| spellingShingle | optimization methods algorithms adaptive signal processing Arimoto–Blahut algorithm Adaptive filters Niesen, Urs Shah, Devavrat Wornell, Gregory W. Adaptive alternating minimization algorithms |
| title | Adaptive alternating minimization algorithms |
| title_full | Adaptive alternating minimization algorithms |
| title_fullStr | Adaptive alternating minimization algorithms |
| title_full_unstemmed | Adaptive alternating minimization algorithms |
| title_short | Adaptive alternating minimization algorithms |
| title_sort | adaptive alternating minimization algorithms |
| topic | optimization methods algorithms adaptive signal processing Arimoto–Blahut algorithm Adaptive filters |
| url | http://hdl.handle.net/1721.1/53588 https://orcid.org/0000-0003-0737-3259 https://orcid.org/0000-0001-9166-4758 |
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