sample_yalmip_sdpt3.m

 補足説明で説明した問題を

により実装.
実行結果

>> sample_yalmip_sdpt3

 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      prim-obj      dual-obj    cputime
-------------------------------------------------------------------
 0|0.000|0.000|5.4e+002|9.5e+001|1.4e+004| 0.000000e+000  0.000000e+000| 0:0:00| chol  1  1 
 1|0.850|0.925|8.1e+001|7.3e+000|1.9e+003|-2.856643e-001 -5.375930e+001| 0:0:00| chol  1  1 
 2|0.673|0.894|2.6e+001|7.8e-001|6.9e+002|-5.030134e-001 -5.958118e+001| 0:0:00| chol  1  1 
 3|0.628|0.887|9.8e+000|8.9e-002|2.9e+002|-2.573922e-001 -3.891857e+001| 0:0:00| chol  1  1 
 4|0.650|1.000|3.4e+000|1.0e-004|1.2e+002|-2.258608e-001 -1.644511e+001| 0:0:00| chol  1  1 
 5|0.906|0.906|3.2e-001|1.8e-005|1.4e+001|-3.275003e-001 -5.542629e+000| 0:0:00| chol  1  1 
 6|0.531|1.000|1.5e-001|1.0e-006|8.2e+000|-7.029058e-001 -3.017501e+000| 0:0:01| chol  1  1 
 7|0.845|0.977|2.3e-002|1.2e-007|1.7e+000|-6.227445e-001 -1.327250e+000| 0:0:01| chol  1  1 
 8|0.653|1.000|8.1e-003|4.7e-003|9.1e-001|-6.599637e-001 -1.073696e+000| 0:0:01| chol  1  1 
 9|0.782|1.000|1.8e-003|1.6e-003|3.4e-001|-7.194625e-001 -9.028305e-001| 0:0:01| chol  1  1 
10|0.679|1.000|5.7e-004|3.5e-004|1.3e-001|-7.527889e-001 -8.135413e-001| 0:0:01| chol  1  1 
11|0.588|0.689|2.3e-004|2.2e-004|8.1e-002|-7.549313e-001 -7.995279e-001| 0:0:01| chol  1  1 
12|0.462|1.000|1.3e-004|4.7e-005|5.6e-002|-7.574675e-001 -7.904237e-001| 0:0:01| chol  1  2 
13|0.640|0.778|4.5e-005|3.5e-005|3.5e-002|-7.611090e-001 -7.841262e-001| 0:0:01| chol  2  2 
14|0.682|1.000|1.4e-005|9.0e-006|1.9e-002|-7.655458e-001 -7.801834e-001| 0:0:01| chol  2  2 
15|1.000|0.779|1.3e-011|4.9e-006|7.4e-003|-7.698532e-001 -7.772960e-001| 0:0:01| chol  2  2 
16|0.979|0.979|5.9e-013|1.0e-007|1.6e-004|-7.748359e-001 -7.749926e-001| 0:0:01| chol  2  2 
17|0.976|0.976|2.3e-012|2.4e-009|3.8e-006|-7.749383e-001 -7.749421e-001| 0:0:01| chol  2  1 
18|1.000|1.000|2.8e-011|1.0e-012|4.5e-007|-7.749405e-001 -7.749410e-001| 0:0:01| chol  2  2 
19|1.000|1.000|3.0e-012|1.6e-012|8.9e-009|-7.749408e-001 -7.749408e-001| 0:0:01|
  stop: max(relative gap, infeasibilities) < 1.00e-007
-------------------------------------------------------------------
 number of iterations   = 19
 primal objective value = -7.74940791e-001
 dual   objective value = -7.74940799e-001
 gap := trace(XZ)       = 8.89e-009
 relative gap           = 3.48e-009
 actual relative gap    = 3.43e-009
 rel. primal infeas     = 2.95e-012
 rel. dual   infeas     = 1.56e-012
 norm(X), norm(y), norm(Z) = 1.1e+000, 5.0e+002, 7.1e+003
 norm(A), norm(b), norm(C) = 1.9e+002, 2.0e+000, 2.4e+000
 Total CPU time (secs)  = 1.1  
 CPU time per iteration = 0.1  
 termination code       =  0
 DIMACS: 3.0e-012  0.0e+000  1.9e-012  0.0e+000  3.4e-009  3.5e-009
-------------------------------------------------------------------
ans = 
    yalmiptime: 0.1970
    solvertime: 1.3750
          info: 'No problems detected (SDPT3-4)'
       problem: 0
        dimacs: [2.9535e-012 0 2.7624e-012 0 3.4256e-009 3.4844e-009]
gamma_opt =
    0.7749
X_opt =
   66.3096    5.1043 -166.1865  -23.0505   16.0398
    5.1043    1.5470   -8.2860   -5.0885    1.5097
 -166.1865   -8.2860  456.2524   57.9411  -34.8457
  -23.0505   -5.0885   57.9411   80.5351   -4.5477
   16.0398    1.5097  -34.8457   -4.5477    4.8827
Z_opt =
   -6.2692
   -2.5465
   14.4110
    4.0317
   -1.2958
K_opt =
    6.5233   -7.7435    1.7719   -0.2351   -6.8743
    
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