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A sample LMI problem

>> %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
>> % Sample LMI problem
>> %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
>> 
>> load testing/lmi/hinf1        % from Gahinet
>> setpars                       % sets scalefac = 100
>> initvars
>> sdp

tau =   0.9990,     scalefac =      100

iter   p_step      d_step     p_infeas    d_infeas      X.Z         pobj        dobj
  0   0.000e+00   0.000e+00   4.536e+02   3.742e+02   1.400e+05   0.000e+00   0.000e+00
  1   8.702e-01   1.000e+00   5.887e+01   3.553e-15   1.462e+04  -2.311e+00  -1.423e+02
  2   9.964e-01   1.000e+00   2.138e-01   5.040e-14   1.881e+02  -8.974e-02  -1.366e+02
  3   6.524e-01   9.997e-01   7.431e-02   2.807e-14   1.424e+01  -1.268e-01  -5.962e+00
  4   9.296e-01   8.036e-01   5.232e-03   1.974e-14   1.969e+00  -9.935e-01  -2.389e+00
  5   6.838e-01   1.000e+00   1.654e-03   2.169e-14   1.164e+00  -1.614e+00  -2.462e+00
  6   9.780e-01   9.855e-01   3.633e-05   3.224e-14   2.058e-02  -2.029e+00  -2.043e+00
  7   8.210e-01   1.000e+00   6.502e-06   4.463e-14   4.563e-03  -2.032e+00  -2.035e+00
  8   7.948e-01   1.000e+00   1.334e-06   8.362e-14   1.583e-03  -2.033e+00  -2.033e+00
  9   7.530e-01   1.000e+00   3.291e-07   1.996e-13   9.761e-04  -2.032e+00  -2.033e+00
 10   1.465e-02   7.657e-01   3.243e-07   3.405e-13   9.435e-04  -2.032e+00  -2.033e+00
 11   1.473e-01   1.567e-01   8.776e-07   3.623e-13   8.924e-04  -2.032e+00  -2.033e+00
 12   8.588e-01   8.535e-01   2.237e-07   3.358e-13   1.017e-04  -2.033e+00  -2.033e+00
 13   8.159e-01   1.000e+00   2.989e-06   4.530e-13   2.650e-05  -2.033e+00  -2.033e+00
 14   5.789e-01   3.171e-01   1.110e-06   5.029e-13   2.717e-05  -2.033e+00  -2.033e+00
 15   5.643e-03   5.534e-02   1.107e-06   6.097e-13   3.097e-05  -2.033e+00  -2.033e+00
 16   3.933e-01   5.692e-01   7.331e-07   1.436e-12   1.992e-05  -2.033e+00  -2.033e+00
 17   4.891e-01   7.193e-01   3.623e-07   8.719e-13   1.067e-05  -2.033e+00  -2.033e+00
 18   1.000e+00   1.000e+00   2.734e-07   1.033e-12   8.867e-06  -2.033e+00  -2.033e+00
 19   7.159e-01   1.000e+00   1.412e-07   1.974e-12   2.106e-06  -2.033e+00  -2.033e+00
 20   1.000e+00   1.000e+00   6.915e-08   2.002e-12   2.749e-08  -2.033e+00  -2.033e+00
 21   9.990e-01   9.990e-01   2.089e-07   1.097e-12   3.033e-11  -2.033e+00  -2.033e+00
 22   1.000e+00   1.000e+00   2.279e-07   1.079e-12   4.434e-12  -2.033e+00  -2.033e+00
fsdp: stop since limiting accuracy reached.
	(new X is indefinite, hence rejected)

sdp: elapsed time               =   3.43612 seconds
sdp: elapsed cpu time           =   3.36000 seconds
sdp: flops                      =   1.84914e+06
sdp: Number of iterations       =   22
sdp: final value of X.Z         =   4.434e-12
sdp: final primal infeasibility =   2.279e-07
sdp: final dual infeasibility   =   1.079e-12
sdp: primal objective value     =  -2.0326830740965565e+00
sdp: dual objective value       =  -2.0326415068447088e+00
>> primalcond(A,blk,X,1.0e-06);  % check if primal degenerate
primalcond =   1.699e+15
>> dualcond(A,blk,Z,1.0e-06);    % check if dual degenerate
dualcond =   9.738e+00



Madhu Nayakkankuppam
Fri Mar 28 00:48:56 EST 1997