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GSOS: Gauss-Seidel Operator Splitting Algorithm for Multi-Term Nonsmooth Convex Composite Optimization
Li Shen · Wei Liu · Ganzhao Yuan · Shiqian Ma

Mon Aug 07 01:30 AM -- 05:00 AM (PDT) @ Gallery #42

In this paper, we propose a fast {\bf{G}}auss-{\bf{S}}eidel {\bf{O}}perator {\bf{S}}plitting (GSOS) algorithm for addressing multi-term nonsmooth convex composite optimization, which has wide applications in machine learning, signal processing and statistics. The proposed GSOS algorithm inherits the advantage of the Gauss-Seidel technique to accelerate the optimization procedure, and leverages the operator splitting technique to reduce the computational complexity. In addition, we develop a new technique to establish the global convergence of the GSOS algorithm. To be specific, we first reformulate the iterations of GSOS as a two-step iterations algorithm by employing the tool of operator optimization theory. Subsequently, we establish the convergence of GSOS based on the two-step iterations algorithm reformulation. At last, we apply the proposed GSOS algorithm to solve overlapping group Lasso and graph-guided fused Lasso problems. Numerical experiments show that our proposed GSOS algorithm is superior to the state-of-the-art algorithms in terms of both efficiency and effectiveness.

Author Information

Li Shen (School of Mathematics, South China University of Technology)
Wei Liu (Tencent AI Lab)
Ganzhao Yuan (SYSU)
Shiqian Ma (The Chinese University of Hong Kong)

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