TY - JOUR AU - Sun, Hongchun AU - Sun, Min AU - Zhou, Houchun PY - 2016 TI - A proximal splitting method for separable convex programming and its application to compressive sensing JO - Journal of Nonlinear Sciences and Applications SP - 392--403 VL - 9 IS - 2 AB - 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. SN - ISSN 2008-1901 UR - http://dx.doi.org/10.22436/jnsa.009.02.05 DO - 10.22436/jnsa.009.02.05 ID - Sun2016 ER - TY - BOOK TI - Constrained Optimization and Lagrange Multiplier Methods AU - D. P. Bertsekas PB - Academic Press PY - 1982 DA - 1982// CY - New York-London ID - Bertsekas1982 ER - TY - JOUR TI - Linearized alternating directions method for l1-norm inequality constrained \(l_1\)-norm minimization AU - S. Cao AU - Y. Xiao AU - H. Zhu JO - Appl. Numer. Math. PY - 2014 DA - 2014// VL - 85 ID - Cao2014 ER - TY - BOOK TI - Convergence analysis of the Peaceman-Rachford splitting method for nonsmooth convex optimization AU - D. R. Han AU - X. M. Yuan PB - J. Optim. Theory Appl. PY - Under-revision DA - Under-revision// CY - ID - HanUnder-revision ER - TY - JOUR TI - A strictly contractive Peaceman-Rachford splitting method for convex programming AU - B. He AU - H. Liu AU - Z. Wang AU - X. Yuan JO - SIAM J. Optim. PY - 2014 DA - 2014// VL - 24 ID - He2014 ER - TY - BOOK TI - A strictly contractive Peaceman-Rachford splitting method with logarithmic-quadratic proximal regularization for convex programming AU - M. Li AU - X. Yuan PB - Math. Oper. Res., 2015 PY - 2015 DA - 2015// CY - ID - Li2015 ER - TY - JOUR TI - Splitting algorithms for the sum of two nonlinear operators AU - P. L. Lions AU - B. Mercier JO - SIAM J. Num. Anal. PY - 1979 DA - 1979// VL - 16 ID - Lions1979 ER - TY - JOUR TI - The numerical solution of parabolic elliptic differential equations AU - D. H. Peaceman AU - H. H. Rachford JO - SIAM J. Appl. Math. PY - 1955 DA - 1955// VL - 3 ID - Peaceman1955 ER - TY - JOUR TI - A proximal Peaceman-Rachford splitting method for compressive sensing AU - M. Sun AU - J. Liu JO - J. Appl. Math. Comput. PY - 2015 DA - 2015// VL - ID - Sun2015 ER -