========================
  The SDPA-Data-Format
========================

SDP-solvers typically use the standard sdpa-format (*.dat-s) for the problem 
instances. For solving mixed-integer SDPs we need to extend the format. The 
sdpa-format is a sparse format, so zeros can be omitted. 
The format models problems in the following standard form:
	min c^T*x
    s.t. sum_i A_i*x_i - A_0 =  Y
                           Y >= 0

Example:
--------------------------------------------------------------------------------
3 			= number of variables
4 			= number of blocks
5 5 5 -10	= block sizes, first three blocks are SDP-blocks with matrix size 
			  5x5. Last block is an lp-block with 10 inequalities. In lp-blocks 
			  only diagonal entries in the matrix are allowed.
0 0 1 		= these are the coefficients c_i of the objective function. There 
			  should be number of variables many.
0 5 5 5 2
1 1 1 1 5
2 2 1 4 3
3 5 5 5 1
...
*INTEGER*
*1
*3
--------------------------------------------------------------------------------

Matrix entries are given in the following format:
n b i j v
n = number of variables (0 stands for the rhs, i.e. the constant terms)
b = number of block
i j = position in matrix
v = coefficient or value

All inequalities are >=
A detailled description of the SDPA-format can be found here: 
http://euler.nmt.edu/~brian/sdplib/FORMAT. 

All matrices must be symmetric, so only the upper or the lower triangle of a 
matrix should be given. Only one entry per variable and position is allowed.

*-------------*
*  EXTENSION  *
*-------------*
Our extension starts with '*INTEGER*'. This signals a new section in the 
sdpa-file. Afterwards there is one line per integer variable, beginning with 
a '*'. Be careful as the format is 1-based. If your variables are binary, you  
have to model the bounds on the variables in an lp-block, i.e. x_i >=0 and  
-x_i>=-1. Lines beginning with '*' are treated as  comments by common  
SDPA-readers, so they will have no problem with our files. Our extension will be
ignored.

________________________________________________________________________________
References:

[1] Borchers, Brian. SDPLIB 1.2, a library of semidefinite programming test 
	problems. Optimization Methods and Software, volume 11, number 1-4, 
    pages 683-690, 1999, doi = 10.1080/10556789908805769.