期刊
ASIA-PACIFIC JOURNAL OF OPERATIONAL RESEARCH
卷 32, 期 4, 页码 -出版社
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0217595915500244
关键词
Convex minimization problems; alternating direction method of multipliers; semi-proximal; strongly convex
资金
- National Natural Science Foundation of China [11001053]
- Program for New Century Excellent Talents in University [NCET-12-0111]
- Qing Lan Project
- Ministry of Education, Singapore [R-146-000-194-112]
In this paper, we present a semi-proximal alternating direction method of multipliers (sPADMM) for solving 3-block separable convex minimization problems with the second block in the objective being a strongly convex function and one coupled linear equation constraint. By choosing the semi-proximal terms properly, we establish the global convergence of the proposed sPADMM for the step-length tau is an element of (0, (1 + root 5)/2) and the penalty parameter sigma is an element of (0, +infinity). In particular, if sigma > 0 is smaller than a certain threshold and the first and third linear operators in the linear equation constraint are injective, then all the three added semi-proximal terms can be dropped and consequently, the convergent 3-block sPADMM reduces to the directly extended 3-block ADMM with tau is an element of (0, (1 + root 5)/2).
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