CSDP

Author: Borchers
Version 3.2, 12/15/2000;
Available: yes, from http://www.nmt.edu/ borchers/csdp.html
Key paper: [3]
Features: infeasible predictor-corrector variant of a primal dual method based on the H..K..M direction
Language, Input format: C; SDPA
Error computations: yes
Solves: SDP

CSDP consists of a callable library and standalone solver for SDP problems. It is not applicable to problems with second order cone constraints. The code uses a predictor-corrector variant of the primal-dual method of Helmberg, Rendl, Vanderbei, and Wolkowicz [14] and Kojima, Shindoh, and Hara [17]. CSDP is suited to the solution of small and medium size SDPs with general structure. The algorithm supports matrices with block diagonal structure as well as linear programming variables which are expressed as a diagonal block within the SDP problem.

CSDP is written in portable ANSI C with calls to subroutines from either the Linpack or LAPACK libraries. The required Linpack routines are supplied with the code. However, improved performance can be obtained by using BLAS and LAPACK libraries that have been optimized for a particular computer.

The stopping criteria are:

• $\frac{\vert \langle c, x \rangle - b^T y \vert }{1+ \vert b^T y \vert } < 10^{-7}$ and
• $\frac{\Vert \mathcal{A}x - b\Vert _{2}}{1 + \Vert b \Vert _{2}} < 10^{-7}$ and
• $\frac{\Vert \mathcal{A}^* y -c + z \Vert _{2}}{1 + \Vert c\Vert _{2}} < 10^{-7}.$

In addition, CSDP maintains positive definite $X$ and $Z$ matrices at all times. CSDP checks this by computing the Cholesky factorizations of $X$ and $Z$.