Routines that create the SDPCone object, set the data, and get the solution for problems.

#include dsdp5.h

In DSDP Standard Form, a semidefinite program is given by the pair of problems

$\begin{array}{llllllllll} (P) \ \ \ & \mbox{minimize} & {\displaystyle \sum_{j=0}^{n_b-1} C_j \bullet X_j } &\mbox{subject to}& {\displaystyle \sum_{j=0}^{n_b-1} A_{i,j} \bullet X_{j} = b_i } ,& i=1,\ldots, m, & & X_j \succeq 0, \\ \end{array}$

$\begin{array}{lllllllll} (D) \ \ \ & \mbox{maximize} & {\displaystyle \sum_{i=1}^m b_i \ y_i } &\mbox{subject to}&{\displaystyle \sum_{i=1}^m A_{i,j}y_i + S_{j} } = C_{j}, & j=0, \ldots, n_b-1, & S_j \succeq 0 \\ \end{array}$

where the data $A_{i,j}$ and are symmetric matrices of the same dimension and the inner product of two $n \times n$ matrices $C=(c_{k,l})$ and $X=(x_{k,l})$ is defined by $C \bullet X := trace (C^T X) = \sum_{k,l}c_{k,l} x_{k,l}$ .

Blocks are labelled from 0 to nblocks, where nblocks is the total number of blocks in the SDPCone object.

Variables y are numbered 1 through m. Variable 0 designates the C matrices, which are also denoted $A_{0,j}$ .

By default, this cone represents symmetric $n \times n$ matrices in packed symmetric format. This format uses an array of length and orders the the elements of the matrix as follows:

$\begin{array}{llllllll} [ a_{1,1} & a_{2,1} & a_{2,2} & a_{3,1} & a_{3,2} & a_{3,3} & \ldots & a_{n,n} ] \\ \end{array}.$

Return values

0	if successful