Solving large-scale least squares semidefinite programming by alternating direction methods. (English) Zbl 1243.49039

He, Bingsheng; Xu, Minghua; Yuan, Xiaoming

SIAM J. Matrix Anal. Appl. 32, No. 1, 136-152 (2011).

Summary: The well-known Least Squares SemiDefinite Programming (LSSDP) problem seeks the nearest adjustment of a given symmetric matrix in the intersection of the cone of positive semidefinite matrices and a set of linear constraints, and it captures many applications in diversing fields. The task of solving large-scale LSSDP with many linear constraints, however, is numerically challenging. This paper mainly shows the applicability of the classical Alternating Direction Method (ADM) for solving LSSDP and convinces the efficiency of the ADM approach. We compare the ADM approach with some other existing approaches numerically, and we show the superiority of ADM for solving large-scale LSSDP.

MSC:

49M29	Numerical methods involving duality
90C22	Semidefinite programming
90C06	Large-scale problems in mathematical programming
90C25	Convex programming

Keywords:

least squares semidefinite matrix; alternating direction method; variational inequality; large-scale problems

Software:

SeDuMi; QSDP; SDPT3; CSDP