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qinzhen724

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[求助] Matlab中用fmincon求解最小值问题，调试了好多次，一直找不到可行解，求大神指导已有2人参与

用fmincon求解最小值问题（1个目标函数、9个变量、6个线性等式约束），一直都是No feasible solution，不知道本身无解还是什么问题。

x0=[4000;4000;2000;500;100;10;10;10;10];
A=[]; b=[];
Aeq=[-88.840439250000020, 20.679950666666663, -2.158236236666667e+02, -3.601469919166667e+02, -36.694763666666690, 21.462819666666660, -13.261596999999995, 7.477251833333336, -1.023975406666667e+02;
0.012, 0,    0,    0.012,  0.012, 0,    0,    0, 0.012;
0,    0.002,  0.002,    0, 0.004, 0, 0.003,  0.002, 0;
0.016, 0, 0.016, 0.032, 0,    0,    0,    0, 0.016;
0,       0,    0,    0,    0, 0.028,  0.014, 0,    0;
0,       0,    0,    0,    0,    0,    0, 0.032, 0.032]
beq=[4588048.12066667;
      171.600000000000;
      21.5666666666667;
      241.933333333333;
      2.10000000000000;
      0.600000000000000]
VLB=[0.001;0.001;0.001;0.001;0.001;0.001;0.001;0.001;0.001];
VUB=[6601.833333;4978.305556;4978.305556;5172.684028;2489.152778;34.625;69.25;8.65625;8.65625];
options = optimoptions(@fmincon,'Algorithm','interior-point','MaxIter',5000);
[x,fval,exitflag,output]=fmincon(@Gibbsfun,x0,A,b,Aeq,beq,VLB,VUB,[],options)

%%目标函数为myobjfun
function G=myobjfun(x)
deltaG1=-8.841665127258336e+04; deltaG2=-1.661952727160000e+05;
deltaG3=5.504948170966668e+04; deltaG4=-1.666712325249982e+03;
deltaG5=1.092642304030001e+05; deltaG6=-2.281491138470000e+05;
deltaG7=1.169078584030000e+05; deltaG8=1.087887085851667e+05;
deltaG9=4.941138012599998e+04;
G=x(1)*(deltaG1+8314*log(x(1)/sum(x)*1.2))+x(2)*(deltaG2+8314*log(x(2)/sum(x)*1.2))...
+x(3)*(deltaG3+8314*log(x(3)/sum(x)*1.2))+x(4)*(deltaG4+8314*log(x(4)/sum(x)*1.2))...
+x(5)*(deltaG5+8314*log(x(5)/sum(x)*1.2))+x(6)*(deltaG6+8314*log(x(6)/sum(x)*1.2))...
+x(7)*(deltaG7+8314*log(x(7)/sum(x)*1.2))+x(8)*(deltaG8+8314*log(x(8)/sum(x)*1.2))...
+x(9)*(deltaG9+8314*log(x(9)/sum(x)*1.2))

计算结果如下：
No feasible solution found.
fmincon stopped because the size of the current step is less than
the default value of the step size tolerance but constraints are not
satisfied to within the default value of the constraint tolerance.

<stopping criteria details>
x =
1.0e+03 *

4.666024308553983
3.857233354391819
2.387214185792911
0.000001000000005
0.000001000000001
0.015465337002847
0.000001000000003
0.008656249999525
0.006364985001793

fval =
-1.006342210855910e+09

exitflag =
-2

output =

      iterations: 70
      funcCount: 710
constrviolation: 5.438285104570996e+06
         stepsize: 9.313859771460607e-10
      algorithm: 'interior-point'
   firstorderopt: 0.043644013275751
   cgiterations: 76
         message: 'No feasible solution found.

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1楼 2016-01-22 16:19:43

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qinzhen724

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引用回帖:

4楼: Originally posted by wang_chuan at 2016-01-27 22:30:02
你采用的是MATLAB内置的寻优方法，内点法，此类方法要求被求对象导数存在且容易求得，你的问题不一定符合这个要求。也就是说，你待求解的问题非线性强，不能用数学方法来做，或找不到可行解。建议用粒子群算法自己写 ...

好的，我试试，谢谢

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