You can try SCIP which is a constraint integer programming solver and supports 
quadratic constraints. I started a Sage interface here:

  http://trac.sagemath.org/sage_trac/ticket/10879

>From the ticket description:

"""
"SCIP is currently one of the fastest non-commercial mixed integer programming 
(MIP) solvers. It is also a framework for Constraint Integer Programming and 
branch-cut-and-price. It allows total control of the solution process and the 
access of detailed information down to the guts of the solver." --  
http://scip.zib.de/

Features interesting to Sage:

 - SCIP is pretty fast for Mixed Integer Programming
- SCIP is a Constraint Integer Programming solver and allows non-linear 
constraints
 - SCIP's source code is available

However, we don't have the right to redistribute the SCIP source code. Thus, 
the attached SPKG is empty except for the spkg-install script etc.

To build a SCIP for Sage do:

- download the ZIB Optmisation Suite from  
http://zibopt.zib.de/download.php?fname=ziboptsuite-2.0.1.tgz
- place the files scip-2.0.1.tgz and soplex-1.5.0.tgz in the src/ subdirectory 
of the attached SPKG
- install the SPKG
- apply the attached patch and sage -b

KNOWN ISSUES

- Sage crashes when SCIP variables are printed with SIGSEGV on OSX. It works 
fine under Linux.

- the following doctests fail
 sage -t  -long -force_lib 
devel/sage/doc/en/thematic_tutorials/linear_programming.rst # 1 doctests 
failed
 sage -t  -long -force_lib devel/sage/sage/graphs/digraph.py # 1 doctests 
failed
 sage -t  -long -force_lib devel/sage/sage/numerical/mip.pyx # 3 doctests 
failed

- printing of quadratic constraints does not work yet.
"""

The patch probably also bitrotted a bit by now. But I'd be very happy to see 
it completed, so I'm happy to help anyone who'd attempt to finish it. Also, 
the SCIP developers are happy to help out if we have questions etc.

On Wednesday 30 May 2012, Ruslan Kiyanchuk wrote:
> Thanks. Can you recommend any good tool other than Sage (since it doesn't
> have such interfaces yet) that would handle quadratic inequalities?
> 
> On Wed, May 30, 2012 at 3:32 PM, Nathann Cohen 
<[email protected]>wrote:
> > Well, no it is not. We would need an interface with quadratic solvers to
> > do that, and all we have now are *linear* solvers. At least through the
> > MILP class.
> > 
> > Nathann
> > 
> > --
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Cheers,
Martin

--
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