1,723,227 research outputs found
Convergence in Distribution of Randomized Algorithms: The Case of Partially Separable Optimization
No full textWe present a Markov-chain analysis of blockwise-stochastic algorithms for solving partially
block-separable optimization problems. Our main contributions to the extensive literature on these methods are statements about the Markov operators and distributions behind the iterates of stochastic algorithms, and in particular the regularity of Markov operators and rates of convergence of the distributions
of the corresponding Markov chains. This provides a detailed characterization of the moments of the sequences beyond just the expected behavior. This also serves as a case study of how randomization restores
favorable properties to algorithms that iterations of only partial information destroys. We demonstrate
this on stochastic blockwise implementations of the forward-backward and Douglas-Rachford algorithms
for nonconvex (and, as a special case, convex), nonsmooth optimization
Variational Numerical Analysis
No full textThis monograph covers numerical analysis using the tools of variational analysis to handle nonsmooth and nonconvex problems in continuous optimizatio
Convergence in Distribution of Randomized Algorithms: The Case of Partially Separable Optimization
No full textWe present a Markov-chain analysis of blockwise-stochastic algorithms for solving partially block-separable optimization problems. Our main contributions to the extensive literature on these methods are statements about the Markov operators and distributions behind the iterates of stochastic algorithms, and in particular the regularity of Markov operators and rates of convergence of the distributions of the corresponding Markov chains. This provides a detailed characterization of the moments of the sequences beyond just the expected behavior. This also serves as a case study of how randomization restores favorable properties to algorithms that iterations of only partial information destroys. We demonstrate this on stochastic blockwise implementations of the forward-backward and Douglas-Rachford algorithms for nonconvex (and, as a special case, convex), nonsmooth optimization
Variational Numerical Analysis
No full textThis monograph covers numerical analysis using the tools of variational analysis to handle nonsmooth and nonconvex problems in continuous optimizatio
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