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A class of parallel splitting method inspired by pseudo search direction for separable convex programming

Shengjie Xu(xsjnsu***at***163.com)

Abstract: We present a class of parallel splitting pseudo proximal point algorithm for solving the separable convex minimization problem with linear constraints, whose objective function is the sum of m individual subfunctions without coupled variables. In real computations, it is well known that algorithms with Jacobian structure can achieve parallel computing but have low efficiency; algorithms with Gauss-Seidel structure have efficient numerical performance but cannot perform parallel computing. Inspired by a mixture of two types of algorithms, the novel method needs only a simple back substitution procedure to the original parallel splitting step. Furthermore, we also establish its global convergence and a worst-case O(1/t) convergence rate from a perspective of prediction-correction method. Finally, taking a sparse matrix minimization problem arising in the statistical learning as an example, we show the efficient performance of the purposed method.

Keywords: Convex optimization, Convergence rate, Operator splitting method, Parallel computing, Proximal point algorithm

Category 1: Convex and Nonsmooth Optimization

Category 2: Convex and Nonsmooth Optimization (Convex Optimization )

Category 3: Optimization Software and Modeling Systems (Parallel Algorithms )


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Entry Submitted: 01/10/2020
Entry Accepted: 01/10/2020
Entry Last Modified: 01/10/2020

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