sample_cvx_default.m

　補足説明で説明した問題を

  • LMI パーサ CVX
  • デフォルトの SDP ソルバ （CVX に包含されている SeDuMi がデフォルトとなる）
により実装．
実行結果 

>> sample_cvx_default
 
Calling sedumi: 91 variables, 21 equality constraints
   For improved efficiency, sedumi is solving the dual problem.
------------------------------------------------------------
SeDuMi 1.21 by AdvOL, 2005-2008 and Jos F. Sturm, 1998-2003.
Alg = 2: xz-corrector, Adaptive Step-Differentiation, theta = 0.250, beta = 0.500
eqs m = 21, order n = 19, dim = 165, blocks = 3
nnz(A) = 207 + 0, nnz(ADA) = 441, nnz(L) = 231
 it :     b*y       gap    delta  rate   t/tP*  t/tD*   feas cg cg  prec
  0 :            6.71E+001 0.000
  1 : -1.37E+000 1.63E+001 0.000 0.2434 0.9000 0.9000   1.30  1  1  1.7E+001
  2 : -2.25E+000 4.92E+000 0.000 0.3013 0.9000 0.9000   0.42  1  1  7.7E+000
  3 : -1.97E+000 1.26E+000 0.000 0.2571 0.9000 0.9000   0.66  1  1  2.3E+000
  4 : -1.63E+000 3.41E-001 0.000 0.2697 0.9000 0.9000   0.58  1  1  8.1E-001
  5 : -1.38E+000 9.37E-002 0.000 0.2747 0.9000 0.9000   0.46  1  1  3.1E-001
  6 : -1.22E+000 2.65E-002 0.000 0.2826 0.9000 0.9000   0.46  1  1  1.2E-001
  7 : -1.09E+000 7.03E-003 0.000 0.2652 0.9000 0.9000   0.36  1  1  4.8E-002
  8 : -9.79E-001 1.78E-003 0.000 0.2537 0.9000 0.9000   0.26  1  1  2.0E-002
  9 : -9.06E-001 4.68E-004 0.000 0.2624 0.9000 0.9000   0.24  1  1  8.6E-003
 10 : -8.63E-001 1.41E-004 0.000 0.3010 0.9000 0.9000   0.30  1  1  3.8E-003
 11 : -8.32E-001 4.26E-005 0.000 0.3026 0.9000 0.9000   0.36  1  1  1.7E-003
 12 : -8.12E-001 1.53E-005 0.000 0.3583 0.9000 0.9000   0.41  1  1  8.4E-004
 13 : -7.99E-001 5.69E-006 0.000 0.3731 0.9000 0.9000   0.50  1  1  4.1E-004
 14 : -7.92E-001 2.78E-006 0.000 0.4880 0.9000 0.9000   0.49  1  1  2.6E-004
 15 : -7.86E-001 1.11E-006 0.000 0.4003 0.9000 0.9000   0.64  1  1  1.2E-004
 16 : -7.82E-001 5.55E-007 0.000 0.4991 0.9000 0.9000   0.54  1  1  7.7E-005
 17 : -7.79E-001 2.20E-007 0.000 0.3957 0.9000 0.9000   0.67  1  1  3.6E-005
 18 : -7.77E-001 1.05E-007 0.000 0.4771 0.9000 0.9000   0.55  1  1  2.2E-005
 19 : -7.76E-001 3.86E-008 0.000 0.3680 0.9000 0.9000   0.69  1  1  9.4E-006
 20 : -7.75E-001 2.04E-008 0.000 0.5298 0.9000 0.9000   0.70  2  2  5.5E-006
 21 : -7.75E-001 5.63E-010 0.000 0.0276 0.9890 0.9900   0.97  1  1  1.7E-007
 22 : -7.75E-001 4.92E-012 0.000 0.0087 0.9990 0.9990   0.99  2  2  1.5E-009

iter seconds digits       c*x               b*y
 22      0.4   Inf -7.7494092147e-001 -7.7494090478e-001
|Ax-b| =  1.6e-009, [Ay-c]_+ =  0.0E+000, |x|= 1.1e+000, |y|= 4.0e+003

Detailed timing (sec)
   Pre          IPM          Post
1.560E-002    4.056E-001    0.000E+000    
Max-norms: ||b||=1, ||c|| = 2,
Cholesky |add|=0, |skip| = 0, ||L.L|| = 13129.6.
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +0.774941   %%% gamma
K =
    6.5233   -7.7435    1.7719   -0.2351   -6.8743