sample_cvx_sdpt3.m

　補足説明で説明した問題を

  • LMI パーサ CVX
  • SDP ソルバ SDPT3 （CVX に包含）
により実装．
実行結果 

>> sample_cvx_sdpt3
 
Calling sdpt3: 91 variables, 21 equality constraints
   For improved efficiency, sdpt3 is solving the dual problem.
------------------------------------------------------------

 num. of constraints = 21
 dim. of sdp    var  = 18,   num. of sdp  blk  =  2
*******************************************************************
   SDPT3: Infeasible path-following algorithms
*******************************************************************
 version  predcorr  gam  expon  scale_data
   HKM      1      0.000   1        0    
it pstep dstep pinfeas dinfeas  gap      mean(obj)   cputime
-------------------------------------------------------------------
 0|0.000|0.000|2.1e+002|6.2e+001|9.3e+003| 0.000000e+000| 0:0:01| chol  1  1 
 1|0.850|0.929|3.2e+001|4.5e+000|1.2e+003|-1.856691e+001| 0:0:01| chol  1  1 
 2|0.668|0.892|1.1e+001|5.0e-001|4.4e+002|-2.015165e+001| 0:0:01| chol  1  1 
 3|0.606|0.856|4.2e+000|7.2e-002|2.0e+002|-1.361962e+001| 0:0:01| chol  1  1 
 4|0.581|1.000|1.8e+000|1.0e-004|1.0e+002|-6.796411e+000| 0:0:01| chol  1  1 
 5|0.920|0.893|1.4e-001|2.0e-005|1.1e+001|-2.491115e+000| 0:0:01| chol  1  1 
 6|0.545|1.000|6.5e-002|1.0e-006|6.5e+000|-1.760797e+000| 0:0:01| chol  1  1 
 7|0.846|0.979|1.0e-002|1.3e-002|1.3e+000|-9.648691e-001| 0:0:02| chol  1  1 
 8|0.694|1.000|3.0e-003|2.0e-003|6.0e-001|-8.614559e-001| 0:0:02| chol  1  1 
 9|0.714|0.904|8.7e-004|8.0e-004|2.7e-001|-8.189656e-001| 0:0:02| chol  1  1 
10|0.435|1.000|4.9e-004|1.7e-004|1.8e-001|-7.957387e-001| 0:0:02| chol  1  1 
11|0.626|0.764|1.8e-004|1.4e-004|1.1e-001|-7.834027e-001| 0:0:02| chol  1  1 
12|0.579|1.000|7.7e-005|3.7e-005|6.8e-002|-7.768664e-001| 0:0:02| chol  2  2 
13|0.669|0.575|2.6e-005|3.1e-005|4.2e-002|-7.739740e-001| 0:0:02| chol  1  2 
14|0.540|1.000|1.2e-005|5.1e-006|2.6e-002|-7.729402e-001| 0:0:02| chol  2  2 
15|0.728|0.825|3.2e-006|3.2e-006|1.5e-002|-7.724239e-001| 0:0:02| chol  2  2 
16|0.868|1.000|4.2e-007|6.4e-007|2.4e-003|-7.743436e-001| 0:0:02| chol  2  2 
17|1.000|1.000|2.6e-012|8.5e-008|3.9e-004|-7.748733e-001| 0:0:02| chol  2  2 
18|0.980|0.985|1.1e-012|1.2e-009|7.2e-006|-7.749393e-001| 0:0:02| chol  2  2 
19|1.000|1.000|2.6e-013|1.0e-012|3.1e-007|-7.749408e-001| 0:0:02| chol  2  2 
20|1.000|1.000|4.0e-012|1.0e-012|1.4e-008|-7.749408e-001| 0:0:02|
  stop: max(relative gap, infeasibilities) < 1.49e-008
-------------------------------------------------------------------
 number of iterations   = 20
 primal objective value = -7.74940787e-001
 dual   objective value = -7.74940801e-001
 gap := trace(XZ)       = 1.37e-008
 relative gap           = 5.36e-009
 actual relative gap    = 5.36e-009
 rel. primal infeas     = 3.97e-012
 rel. dual   infeas     = 1.00e-012
 norm(X), norm(y), norm(Z) = 1.1e+000, 4.0e+003, 7.1e+003
 norm(A), norm(b), norm(C) = 9.9e+001, 2.0e+000, 2.4e+000
 Total CPU time (secs)  = 2.1  
 CPU time per iteration = 0.1  
 termination code       =  0
 DIMACS: 4.0e-012  0.0e+000  1.2e-012  0.0e+000  5.4e-009  5.4e-009
-------------------------------------------------------------------
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +0.774941    %%% gamma
K =
    6.5233   -7.7435    1.7719   -0.2351   -6.8743
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