A Schur Complement Based Semi-Proximal ADMM for Convex Quadratic Conic Programming and Extensions

Understand

This paper is devoted to the design of an efficient and convergent {semi-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 semi-proximal ADMM can be employed to solve their primal form in a straightforward way.
• However, it is known that it is more efficient to apply the directly extended multi-block semi-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 semi-proximal ADMM that is more efficient than the directly extended semi-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)].