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Special Lecture - 10/24, 2:30PM, Duncan Hall 3092

Ernest Ryu

Department of Mathematics

"Proximal-Proximal-Gradient Method"

We present the proximal-proximal-gradient method (PPG), a novel optimization method that is simple to implement and simple to parallelize. PPG generalizes the proximal-gradient method and ADMM and is applicable to minimization problems written as a sum of many differentiable and many non- differentiable convex functions. The non-differentiable functions can be coupled. We furthermore present a related stochastic variation, which we call stochastic PPG (S-PPG). S-PPG can be interpreted as a generalization of Finito and MISO over to the sum of many coupled non-differentiable convex functions. We present many applications that can benefit from PPG and S-PPG and prove convergence for both methods. We demonstrate the empirical effectiveness of both methods through experiments on a CUDA GPU. A key strength of PPG and S-PPG is, compared to existing methods, their ability to directly handle a large sum of non-differentiable non-separable functions with a constant stepsize independent of the number of functions. Such non-diminishing stepsizes allows them to be fast.

Department of Computational and Applied Mathematics
6100 Main MS-134   Houston, TX 77005   713.348.4805

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