Adaptive alternating minimization algorithms
Author(s)Niesen, Urs; Shah, Devavrat; Wornell, Gregory W.
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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.
DepartmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
IEEE Transactions on Information Theory
Institute of Electrical and Electronics Engineers
Niesen, U., D. Shah, and G.W. Wornell. “Adaptive Alternating Minimization Algorithms.” Information Theory, IEEE Transactions on 55.3 (2009): 1423-1429. © 2009 IEEE
Final published version
optimization methods, algorithms, adaptive signal processing, Arimoto–Blahut algorithm, Adaptive filters