2015-10-16Buch DOI: 10.18452/3074
Parallel stochastic optimization based on descent algorithms
This study addresses the stochastic optimization of a function unknown in closed form which can only be estimated based on measurements or simulations. We consider parallel implementations of a class of stochastic optimization methods that consist of the iterative application of a descent algorithm to a sequence of approximation functions converging in some sense to the function of interest. After discussing classical parallel modes of implementations (Jacobi, Gauss-Seidel, random, Gauss-Southwell), we devise effort-saving implementation modes where the pace of application of the considered descent algorithm along individual coordinates is coordinated with the evolution of the estimated accuracy of the convergent function sequence. It is shown that this approach can be regarded as a Gauss-Southwell implementation of the initial method in an augmented space. As an example of application we study the distributed optimization of stochastic networks using a scaled gradient projection algorithm with approximate line search, for which asymptotic properties are derived.
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