| Academic lectures:A Schur Complement Based Proximal ADMM for Convex Quadratic Conic Programming and Extensions |
| Published date：2014-07-16 Provided by：School of Science |
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Title: A Schur Complement Based Proximal ADMM for Convex Quadratic Conic Programming and Extensions
Guest Speaker：Professor Sun Defeng, National University of Singapore
Time：2014-7-4, 10:30 – 11:30
Location：SY102
Content &Introduction：
This paper is devoted to the design of an efficient and convergent proximal alternating direction method of multipliers (ADMM) for finding a solution of low to medium accuracy to convex quadratic conic programming and related problems. For this class of problems, the convergent two block proximal ADMM can be employed to solve their primal form in a straightforward way. However, it is widely known that it is more efficient to apply the directly extended multi-block (proximal) ADMM, though its convergence is not guaranteed, to the dual form of these problems. Naturally, one may ask the following question: can one construct a convergent multi-block (proximal) ADMM that is even much more efficient than the directly extended (proximal) ADMM? Indeed, for linear conic programming with 4-block constraints this has been shown to be achievable in a recent paper by Sun, Toh and Yang [arXiv preprint arXiv:1404.5378, (2014)]. Inspired by the aforementioned work and with the convex quadratic conic programming in mind, we propose a Schur complement based convergent (proximal) ADMM for solving convex programming, with a coupling linear equality constraint, whose objective function is the sum of two proper closed convex functions plus an arbitrary number of convex quadratic or linear functions. Our convergent (proximal) ADMM is particularly suitable for solving convex quadratic semidefinite programming (QSDP) with constraints of linear equalities, a positive semidefinite cone and a convex polyhedral set. The efficiency of our proposed algorithm is demonstrated by extensive numerical experiments for various examples including QSDP. [This is a joint work with Xudong Li and Kim-Chuan. |