A proximal splitting method for separable convex programming and its application to compressive sensing


Authors

Hongchun Sun - School of Sciences, Linyi University, Shandong, 276005, P. R. China. Min Sun - School of Mathematics and Statistics, Zaozhuang University, Shandong, 277160, P. R. China. Houchun Zhou - School of Sciences, Linyi University, Shandong, 276005, P. R. China.


Abstract

Recently, by taking full exploitation to the special structure of the separable convex programming, some splitting methods have been developed. However, in some practical applications, these methods need to compute the inverse of a matrix, which maybe slow down their convergence rate, especially when the dimension of the matrix is large. To solve this issue, in this paper we shall study the Peaceman-Rachford splitting method (PRSM) by adding a proximal term to its first subproblem and get a new method named proximal Peaceman-Rachford splitting method (PPRSM). Under mild conditions, the global convergence of the PPRSM is established. Finally, the effeciency of the PPRSM is illustrated by testing some applications arising in compressive sensing.


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