[Csdp] Puzzling result using icc

[Brian Borchers]

I ran my quadruple precision of CSDP on Ron's problem, and got:

Iter: 23 Ap: 7.85e-01 Pobj:  3.2920448e-01 Ad: 9.53e-01 Dobj:  3.2920448e-01 
Success: SDP solved
Primal objective value: 3.292044793644429146e-01 
Dual objective value: 3.292044793644470224e-01 
Relative primal infeasibility: 3.78e-23 
Relative dual infeasibility: 1.68e-29 
Real Relative Gap: 2.48e-15 
XZ Relative Gap: 2.48e-15 
DIMACS error measures: 1.46e-22 0.00e+00 2.16e-29 0.00e+00 2.48e-15 2.48e-15

So, I don't think that there's anything particularly wrong with the 
problem itself.  
 
I haven't yet tried building the code with icc 11, so I can't really
comment on what might have gone wrong there.  It's not uncommon for
compilers to produce buggy code with high levels of optimization. Or,
in what appears to be almost the same thing, for buggy code that works
with one compiler to break under another compiler that performs more
agressive (but legal) optimizations that reveal the bug.  
 
I should also say that this problem is so extremely small that doing
speed comparisons with it is a bad idea- some optimizations may result
in code which is much faster for large problems but slower for
extremely small problems.  Since what we normally want to is fast
performance on big long running problems, that's actually a good
thing, even if it means that it takes an extra fraction of a second to
solve a very small problem.