🚀 go-pugleaf

I have a linear programming problem (in fact an integer programming
problem, but I thought I would experiment with the relaxation first to
get some feel for these things).

It is very simple:

	Minimize	Sum x_i

	subject to	0 <= x_i <= 1
			Ax > j


	where A is a symmetric matrix with all row and column sums
	equal, and j is the all-ones vector.


Thing is, the solution of this is obvious - the best thing is to put

		x_i = 1/r		where r is the row sum of A


So, I took a 243 x 243 example of this problem and gave it to 
NAG routine E04MBF.

Funny thing was though - instead of quickly giving me the obvious
solution, it gave a far-from-optimal INTEGRAL feasible point and then
stopped, saying that it had made too many iterations without changing
the trial solution.


Three questions:

	1. Why does it behave like this?

	2. What do I do to make it give the right answer

	and thirdly...

	3. when I get down to actually trying to solve the 
	integer linear program, is there any theory around
	that says that symmetric As etc are particularly hard
	(or better still, particularly easy)


    Cheers

    Gordon