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Shengjie Xu(xsjnsu163.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 GaussSeidel 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 worstcase O(1/t) convergence rate from a perspective of predictioncorrection 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 ) Citation: Download: [PDF] Entry Submitted: 01/10/2020 Modify/Update this entry  
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