There is something broken in your sage installation; for me the following 
works:

c=vector(RDF,[-4,-5])
G=matrix(RDF,[[2,1],[1,2],[-1,0],[0,-1]])
h=vector(RDF,[3,3,0,0])
sol=linear_program(c,G,h,solver='glpk')
sol['x']

ouput is

GLPK Simplex Optimizer, v4.60
4 rows, 2 columns, 6 non-zeros
*     0: obj =   0.000000000e+00 inf =   0.000e+00 (2)
*     2: obj =  -9.000000000e+00 inf =   0.000e+00 (0)
OPTIMAL LP SOLUTION FOUND
(1.0, 1.0)

In fact, BUILD_GLPK is set to 1 in the patch applied to cvxopt's setup.py 
at the time sage's cvxopt package
is built, see build/pkgs/cvxopt/patches/setup.py.patch 

We will add a test in the docs, cf. https://trac.sagemath.org/ticket/22217 
that I just opened.


On Friday, January 20, 2017 at 12:11:37 PM UTC, Dima Pasechnik wrote:
>
>
>
> On Friday, January 20, 2017 at 11:44:46 AM UTC, [email protected] wrote:
>>
>> When I run a program it tells me that 
>> `ValueError: invalid option (solver = 'glpk'): cvxopt.glpk is not 
>> installed`. 
>>
>> Then I try to install cvxopt with glpk from source. That is, change 
>> BUILD_GLPK to 1 in the setup.py and then `python setup.py install` in the 
>> sage shell. But it gives me error that
>> `error: command 'gcc' failed with exit status 1`.
>>
>
> This actually should be fixed properly, in the sense that both glpk and 
> cvxopt are standard Sage packages, and so nothing should prevent 
>  BUILD_GLPK=1 in cvxopt settings.
>
> In fact, I am under impression that it was working in the past, see (very 
> old)
> https://trac.sagemath.org/ticket/9598 and 
> https://trac.sagemath.org/ticket/6456
>
>
>

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