TY - JOUR
T1 - A customized Douglas-Rachford splitting algorithm for separable convex minimization with linear constraints
AU - Han, Deren
AU - He, Hongjin
AU - Yang, Hai
AU - Yuan, Xiaoming
N1 - D. Han was supported by the National Natural Science Foundation of China No. 11071122. H. He was supported by the Research Foundation of Hangzhou Dianzi University at Grant No. KYS075612037. X. Yuan was supported by the General Research Fund from Hong Kong Research Grants Council: 203712.
PY - 2014/5
Y1 - 2014/5
N2 - We consider applying the Douglas-Rachford splitting method (DRSM) to the convex minimization problem with linear constraints and a separable objective function. The dual application of DRSM has been well studied in the literature, resulting in the well known alternating direction method of multipliers (ADMM). In this paper, we show that the primal application of DRSM in combination with an appropriate decomposition can yield an efficient structure-exploiting algorithm for the model under consideration, whose subproblems could be easier than those of ADMM. Both the exact and inexact versions of this customized DRSM are studied; and their numerical efficiency is demonstrated by some preliminary numerical results.
AB - We consider applying the Douglas-Rachford splitting method (DRSM) to the convex minimization problem with linear constraints and a separable objective function. The dual application of DRSM has been well studied in the literature, resulting in the well known alternating direction method of multipliers (ADMM). In this paper, we show that the primal application of DRSM in combination with an appropriate decomposition can yield an efficient structure-exploiting algorithm for the model under consideration, whose subproblems could be easier than those of ADMM. Both the exact and inexact versions of this customized DRSM are studied; and their numerical efficiency is demonstrated by some preliminary numerical results.
UR - http://www.scopus.com/inward/record.url?scp=84898547640&partnerID=8YFLogxK
U2 - 10.1007/s00211-013-0580-2
DO - 10.1007/s00211-013-0580-2
M3 - Journal article
AN - SCOPUS:84898547640
SN - 0029-599X
VL - 127
SP - 167
EP - 200
JO - Numerische Mathematik
JF - Numerische Mathematik
IS - 1
ER -