I have a python code to solve the following simple Semidefinite Program:
Input: Two Real 4 x 4 matrices, A and B
Output: 1 - q where q = maximum over all p, such that:
0 < p < 1
A - p B is positive semi-definite
When I view an instance of the above problem in verbose mode, the Python code produces the following message.
10:Channel_Flow pavithran$ python stackoverflow_sdp.py
*** Dualizing the problem... ***
[ #################################################################### ] 100%
[ #################################################################### ] 100%
--------------------------
cvxopt CONELP solver
--------------------------
pcost dcost gap pres dres k/t
0: 5.5546e-01 5.5546e-01 2e+01 3e+00 2e+00 1e+00
1: -4.3006e-01 -7.3065e-02 3e+00 6e-01 3e-01 6e-01
2: -4.9751e+01 2.1091e+00 9e+03 2e+01 8e+00 6e+01
3: -3.4525e+02 7.6511e-02 9e+03 2e+00 1e+00 3e+02
4: -3.4496e+04 7.6337e-02 9e+05 2e+00 1e+00 3e+04
5: -3.4496e+06 7.6337e-02 9e+07 2e+00 1e+00 3e+06
6: -3.4496e+08 7.6337e-02 9e+09 2e+00 1e+00 3e+08
Certificate of dual infeasibility found.
cvxopt status: dual infeasible
*** Dual Solution not found
Traceback (most recent call last):
File "stackoverflow_sdp.py", line 42, in <module>
simple_sdp(A,B)
File "stackoverflow_sdp.py", line 31, in simple_sdp
prob.solve(verbose = 2)
File "/Library/Python/2.7/site-packages/picos/problem.py", line 4246, in solve
raise Exception("\033[1;31m no Primals retrieved from the dual problem \033[0m")
Exception: no Primals retrieved from the dual problem
10:Channel_Flow pavithran$
There are several parameters. I would like to know if it is possible to specify a bound on any of the parameters, to terminate the SDP, except specifying the maximum number of iterations. For instance, can we specify a limit on "gap", "pres", "dres"?
