補足説明で説明した問題を
- LMI パーサ YALMIP
- SDP ソルバ LMILAB (LMI-Lab) ... LMI Control Toolbox が必要
により実装.
>> sample_yalmip_lmilab
Solver for linear objective minimization under LMI constraints
Iterations : Best objective value so far
1
2
3 5.437626
4 2.514236
5 2.041024
6 2.041024
7 1.486270
8 1.267833
9 1.267833
10 1.043977
11 1.043977
12 1.043977
13 0.990801
14 0.990801
15 0.990801
16 0.990801
17 0.891910
18 0.891910
*** new lower bound: 0.435641
19 0.821455
*** new lower bound: 0.559121
20 0.821455
*** new lower bound: 0.627175
21 0.786921
*** new lower bound: 0.681904
22 0.783046
*** new lower bound: 0.756416
23 0.777802
*** new lower bound: 0.759309
24 0.777404
*** new lower bound: 0.764459
25 0.776824
*** new lower bound: 0.768248
26 0.776399
*** new lower bound: 0.770428
27 0.775928
*** new lower bound: 0.771885
28 0.775705
*** new lower bound: 0.772859
29 0.775558
*** new lower bound: 0.773515
30 0.775400
*** new lower bound: 0.773959
31 0.775400
*** new lower bound: 0.774261
32 0.775267
*** new lower bound: 0.774827
Result: feasible solution of required accuracy
best objective value: 0.775267
guaranteed absolute accuracy: 4.40e-004
f-radius saturation: 0.000% of R = 1.00e+009
ans =
yalmiptime: 0.2130
solvertime: 0.3930
info: 'No problems detected (LMILAB)'
problem: 0
dimacs: [NaN NaN 0 0 NaN NaN]
gamma_opt =
0.7753
X_opt =
65.2507 5.0400 -163.3688 -22.6920 15.8043
5.0400 1.5422 -8.1157 -5.0673 1.4954
-163.3688 -8.1157 448.7471 56.9701 -34.2203
-22.6920 -5.0673 56.9701 80.3253 -4.4693
15.8043 1.4954 -34.2203 -4.4693 4.8304
Z_opt =
-6.1621
-2.5363
14.1251
3.9965
-1.2723
K_opt =
6.5131 -7.7392 1.7693 -0.2351 -6.8600