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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 (Tencent)
Wei Liu (Tencent AI Lab)
Ganzhao Yuan (SYSU)
Shiqian Ma (The Chinese University of Hong Kong)
Related Events (a corresponding poster, oral, or spotlight)
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2017 Poster: GSOS: Gauss-Seidel Operator Splitting Algorithm for Multi-Term Nonsmooth Convex Composite Optimization »
Mon. Aug 7th 08:30 AM -- 12:00 PM Room Gallery #42
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