fmincon for multiple variables

Question

Guan Hao 2023-8-23

1
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2011967-fmincon-for-multiple-variables

评论： Guan Hao 2023-8-25

采纳的回答： Matt J

在 MATLAB Online 中打开

Hi,

I want to perform a constrained optimization,that makes fmincon a good option.

However, it returns the error '' fmincon requires all values returned by the functions to be of data type double''.

Y is the objective that I want to optimize,with three variables a1,a2,a3.

function Y = optfun(z)
a1 = z(1);
a2 = z(2);
a3 = z(3);
y1 = abs(vpa("0.129")*a1*sym(1i) + vpa("0.01")*a2*sym(1i) + vpa("8.57e-4")*a3*sym(1i) - vpa("2410.0i")/(vpa("50.0") + vpa("3.7e-5")*a3 + vpa("0.00111")*a2 + vpa("0.0333")*a1) - vpa("2410.0i")/(vpa("50.0") + vpa("2.96e-4")*a3 + vpa("0.00444")*a2 + vpa("0.0667")*a1) - vpa("2410.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) + vpa("25.0") + vpa("96.4i"))/abs(vpa("0.129")*a1*sym(1i) + vpa("0.01")*a2*sym(1i) + vpa("8.57e-4")*a3*sym(1i) + vpa("2410.0i")/(vpa("50.0") + vpa("3.7e-5")*a3 + vpa("0.00111")*a2 + vpa("0.0333")*a1) + vpa("2410.0i")/(vpa("50.0") + vpa("2.96e-4")*a3 + vpa("0.00444")*a2 + vpa("0.0667")*a1) + vpa("2410.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) + vpa("125.0") + vpa("96.4i"));
y2 = abs(vpa("0.173")*a1*sym(1i) + vpa("0.0135")*a2*sym(1i) + vpa("0.00115")*a3*sym(1i) - vpa("3250.0i")/(vpa("50.0") + vpa("3.7e-5")*a3 + vpa("0.00111")*a2 + vpa("0.0333")*a1) - vpa("3250.0i")/(vpa("50.0") + vpa("2.96e-4")*a3 + vpa("0.00444")*a2 + vpa("0.0667")*a1) - vpa("3250.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) + vpa("25.0") + vpa("130.0i"))/abs(vpa("0.173")*a1*sym(1i) + vpa("0.0135")*a2*sym(1i) + vpa("0.00115")*a3*sym(1i) + vpa("3250.0i")/(vpa("50.0") + vpa("3.7e-5")*a3 + vpa("0.00111")*a2 + vpa("0.0333")*a1) + vpa("3250.0i")/(vpa("50.0") + vpa("2.96e-4")*a3 + vpa("0.00444")*a2 + vpa("0.0667")*a1) + vpa("3250.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) + vpa("125.0") + vpa("130.0i"));
y3 = abs(vpa("0.197")*a1*sym(1i) + vpa("0.0153")*a2*sym(1i) + vpa("0.00131")*a3*sym(1i) - vpa("3690.0i")/(vpa("50.0") + vpa("3.7e-5")*a3 + vpa("0.00111")*a2 + vpa("0.0333")*a1) - vpa("3690.0i")/(vpa("50.0") + vpa("2.96e-4")*a3 + vpa("0.00444")*a2 + vpa("0.0667")*a1) - vpa("3690.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) + vpa("25.0") + vpa("148.0i"))/abs(vpa("0.197")*a1*sym(1i) + vpa("0.0153")*a2*sym(1i) + vpa("0.00131")*a3*sym(1i) + vpa("3690.0i")/(vpa("50.0") + vpa("3.7e-5")*a3 + vpa("0.00111")*a2 + vpa("0.0333")*a1) + vpa("3690.0i")/(vpa("50.0") + vpa("2.96e-4")*a3 + vpa("0.00444")*a2 + vpa("0.0667")*a1) + vpa("3690.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) + vpa("125.0") + vpa("148.0i"));
Y = (1-y1)+(1-y3)+(y2);
end

By the way,I want to know is there possibilities to add constration to my objective value?

For example, 0<[y1,y2,y3]<1.

Any help will be appreciate,thx!

1 个评论
显示 -1更早的评论隐藏 -1更早的评论

Stephen23 2023-8-23

Note: the context is explained in the comments here:

https://www.mathworks.com/matlabcentral/answers/2011672-optimization-of-multiple-variables

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Matt J 2023-8-23

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2011967-fmincon-for-multiple-variables#answer_1292522

编辑：Matt J 2023-8-23

在 MATLAB Online 中打开

Y = double( (1-y1)+(1-y3)+(y2) );

But I don't see why you are using vpa and other sym operations. I don't think it really increases precision for you since all your coefficients have substantially less than 32 decimal places.

20 个评论
显示 18更早的评论隐藏 18更早的评论

Guan Hao 2023-8-24

在 MATLAB Online 中打开

@Torsten Thanks for your patience.

Did you mean something like this? It returns a error message that '' fmincon requires all values returned by the functions to be of data type double''.

Sorry,I must misunderstand your meaning...

function [c,ceq] = constraintFcn_new(z)
% My Constraint
% 0.9 <= y1 <= 1
% 0 <= y2 <= 0.1
% 0.9 <= y3 <= 1
a1 = z(1);
a2 = z(2);
a3 = z(3);
y = [abs(- vpa("0.122")*a1*sym(1i) - vpa("0.00895")*a2*sym(1i) - vpa("7.32e-4")*a3*sym(1i) + vpa("1530.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) + vpa("1530.0i")/(vpa("50.0") + vpa("8.0e-6")*a3 + vpa("4.0e-4")*a2 + vpa("0.02")*a1) + vpa("1530.0i")/(vpa("50.0") + vpa("6.4e-5")*a3 + vpa("0.0016")*a2 + vpa("0.04")*a1) + vpa("1530.0i")/(vpa("50.0") + vpa("5.12e-4")*a3 + vpa("0.0064")*a2 + vpa("0.08")*a1) + vpa("1530.0i")/(vpa("50.0") + vpa("2.16e-4")*a3 + vpa("0.0036")*a2 + vpa("0.06")*a1) - vpa("25.0") - vpa("102.0i"))/abs(vpa("0.122")*a1*sym(1i) + vpa("0.00895")*a2*sym(1i) + vpa("7.32e-4")*a3*sym(1i) + vpa("1530.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) + vpa("1530.0i")/(vpa("50.0") + vpa("8.0e-6")*a3 + vpa("4.0e-4")*a2 + vpa("0.02")*a1) + vpa("1530.0i")/(vpa("50.0") + vpa("6.4e-5")*a3 + vpa("0.0016")*a2 + vpa("0.04")*a1) + vpa("1530.0i")/(vpa("50.0") + vpa("5.12e-4")*a3 + vpa("0.0064")*a2 + vpa("0.08")*a1) + vpa("1530.0i")/(vpa("50.0") + vpa("2.16e-4")*a3 + vpa("0.0036")*a2 + vpa("0.06")*a1) + vpa("125.0") + vpa("102.0i"));
abs(- vpa("0.176")*a1*sym(1i) - vpa("0.0129")*a2*sym(1i) - vpa("0.00106")*a3*sym(1i) + vpa("2200.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) + vpa("2200.0i")/(vpa("50.0") + vpa("8.0e-6")*a3 + vpa("4.0e-4")*a2 + vpa("0.02")*a1) + vpa("2200.0i")/(vpa("50.0") + vpa("6.4e-5")*a3 + vpa("0.0016")*a2 + vpa("0.04")*a1) + vpa("2200.0i")/(vpa("50.0") + vpa("5.12e-4")*a3 + vpa("0.0064")*a2 + vpa("0.08")*a1) + vpa("2200.0i")/(vpa("50.0") + vpa("2.16e-4")*a3 + vpa("0.0036")*a2 + vpa("0.06")*a1) - vpa("25.0") - vpa("147.0i"))/abs(vpa("0.176")*a1*sym(1i) + vpa("0.0129")*a2*sym(1i) + vpa("0.00106")*a3*sym(1i) + vpa("2200.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) + vpa("2200.0i")/(vpa("50.0") + vpa("8.0e-6")*a3 + vpa("4.0e-4")*a2 + vpa("0.02")*a1) + vpa("2200.0i")/(vpa("50.0") + vpa("6.4e-5")*a3 + vpa("0.0016")*a2 + vpa("0.04")*a1) + vpa("2200.0i")/(vpa("50.0") + vpa("5.12e-4")*a3 + vpa("0.0064")*a2 + vpa("0.08")*a1) + vpa("2200.0i")/(vpa("50.0") + vpa("2.16e-4")*a3 + vpa("0.0036")*a2 + vpa("0.06")*a1) + vpa("125.0") + vpa("147.0i"));
abs(- vpa("0.223")*a1*sym(1i) - vpa("0.0163")*a2*sym(1i) - vpa("0.00134")*a3*sym(1i) + vpa("2790.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) + vpa("2790.0i")/(vpa("50.0") + vpa("8.0e-6")*a3 + vpa("4.0e-4")*a2 + vpa("0.02")*a1) + vpa("2790.0i")/(vpa("50.0") + vpa("6.4e-5")*a3 + vpa("0.0016")*a2 + vpa("0.04")*a1) + vpa("2790.0i")/(vpa("50.0") + vpa("5.12e-4")*a3 + vpa("0.0064")*a2 + vpa("0.08")*a1) + vpa("2790.0i")/(vpa("50.0") + vpa("2.16e-4")*a3 + vpa("0.0036")*a2 + vpa("0.06")*a1) - vpa("25.0") - vpa("186.0i"))/abs(vpa("0.223")*a1*sym(1i) + vpa("0.0163")*a2*sym(1i) + vpa("0.00134")*a3*sym(1i) + vpa("2790.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) + vpa("2790.0i")/(vpa("50.0") + vpa("8.0e-6")*a3 + vpa("4.0e-4")*a2 + vpa("0.02")*a1) + vpa("2790.0i")/(vpa("50.0") + vpa("6.4e-5")*a3 + vpa("0.0016")*a2 + vpa("0.04")*a1) + vpa("2790.0i")/(vpa("50.0") + vpa("5.12e-4")*a3 + vpa("0.0064")*a2 + vpa("0.08")*a1) + vpa("2790.0i")/(vpa("50.0") + vpa("2.16e-4")*a3 + vpa("0.0036")*a2 + vpa("0.06")*a1) + vpa("125.0") + vpa("186.0i"));];
y1 = y(1);
y2 = y(2);
y3 = y(3);
c(1) = -y1+0.9;
c(2) = y2-0.1;
c(3) = -y3+0.9;
c(4) = y1-1;
c(5) = -y2;
c(6) = y3-1;
ceq=[];
end

Steven Lord 2023-8-24

在 MATLAB Online 中打开

Rather than duplicating your objective function's code in your constraint function, I'd define your objective function to return multiple outputs (the second and later ones being the quantities you're trying to constraint) and call it with multiple outputs in your constraint function.

Note that as per the description of the fun input argument on the fmincon documentation page, if you're using the SpecifyObjectiveGradient and HessianFcn options you may need to push these "supplementary outputs" later in the output list.

Y = optfun([1; 2; 3])
Y = 1.8024
confun([1; 2; 3])
  Y is 1.80239
 y1 is 0.198814
 y2 is 0.198692
 y3 is 0.197487
check: 1.80239
function [Y, y1, y2, y3] = optfun(z)
a1 = z(1);
a2 = z(2);
a3 = z(3);
y1 = abs(vpa("0.129")*a1*sym(1i) + vpa("0.01")*a2*sym(1i) + vpa("8.57e-4")*a3*sym(1i) - vpa("2410.0i")/(vpa("50.0") + vpa("3.7e-5")*a3 + vpa("0.00111")*a2 + vpa("0.0333")*a1) - vpa("2410.0i")/(vpa("50.0") + vpa("2.96e-4")*a3 + vpa("0.00444")*a2 + vpa("0.0667")*a1) - vpa("2410.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) + vpa("25.0") + vpa("96.4i"))/abs(vpa("0.129")*a1*sym(1i) + vpa("0.01")*a2*sym(1i) + vpa("8.57e-4")*a3*sym(1i) + vpa("2410.0i")/(vpa("50.0") + vpa("3.7e-5")*a3 + vpa("0.00111")*a2 + vpa("0.0333")*a1) + vpa("2410.0i")/(vpa("50.0") + vpa("2.96e-4")*a3 + vpa("0.00444")*a2 + vpa("0.0667")*a1) + vpa("2410.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) + vpa("125.0") + vpa("96.4i"));
y2 = abs(vpa("0.173")*a1*sym(1i) + vpa("0.0135")*a2*sym(1i) + vpa("0.00115")*a3*sym(1i) - vpa("3250.0i")/(vpa("50.0") + vpa("3.7e-5")*a3 + vpa("0.00111")*a2 + vpa("0.0333")*a1) - vpa("3250.0i")/(vpa("50.0") + vpa("2.96e-4")*a3 + vpa("0.00444")*a2 + vpa("0.0667")*a1) - vpa("3250.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) + vpa("25.0") + vpa("130.0i"))/abs(vpa("0.173")*a1*sym(1i) + vpa("0.0135")*a2*sym(1i) + vpa("0.00115")*a3*sym(1i) + vpa("3250.0i")/(vpa("50.0") + vpa("3.7e-5")*a3 + vpa("0.00111")*a2 + vpa("0.0333")*a1) + vpa("3250.0i")/(vpa("50.0") + vpa("2.96e-4")*a3 + vpa("0.00444")*a2 + vpa("0.0667")*a1) + vpa("3250.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) + vpa("125.0") + vpa("130.0i"));
y3 = abs(vpa("0.197")*a1*sym(1i) + vpa("0.0153")*a2*sym(1i) + vpa("0.00131")*a3*sym(1i) - vpa("3690.0i")/(vpa("50.0") + vpa("3.7e-5")*a3 + vpa("0.00111")*a2 + vpa("0.0333")*a1) - vpa("3690.0i")/(vpa("50.0") + vpa("2.96e-4")*a3 + vpa("0.00444")*a2 + vpa("0.0667")*a1) - vpa("3690.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) + vpa("25.0") + vpa("148.0i"))/abs(vpa("0.197")*a1*sym(1i) + vpa("0.0153")*a2*sym(1i) + vpa("0.00131")*a3*sym(1i) + vpa("3690.0i")/(vpa("50.0") + vpa("3.7e-5")*a3 + vpa("0.00111")*a2 + vpa("0.0333")*a1) + vpa("3690.0i")/(vpa("50.0") + vpa("2.96e-4")*a3 + vpa("0.00444")*a2 + vpa("0.0667")*a1) + vpa("3690.0i")/(vpa("50.0") + vpa("0.001")*a3 + vpa("0.01")*a2 + vpa("0.1")*a1) + vpa("125.0") + vpa("148.0i"));
% Converting to double after the fact is simpler to type for this example
% than removing all your vpa and sym calls, but for your real code I'd
% perform the removal to avoid involving Symbolic Math Toolbox at all
y1 = double(y1);
y2 = double(y2);
y3 = double(y3);
Y = (1-y1)+(1-y3)+(y2);
end
function confun(z)
% Reuse rather than duplicating
[Y, y1, y2, y3] = optfun(z);
fprintf("  Y is %g\n y1 is %g\n y2 is %g\n y3 is %g\n", Y, y1, y2, y3)
fprintf("check: %g\n", (1-y1)+(1-y3)+y2)
end

Guan Hao 2023-8-24

在 MATLAB Online 中打开

@Steven Lord @Matt J

This is all of my code,it removes all vpa and sym things.

However,when I run the optimization,it seems that the constraints are on a1,a2,a3 again.

function [Y, y1, y2, y3] = optfun_new(z)
Z01=50;
Z02=75;
v=3e+8;
section=100;
L=0.1;
a=L/section;
a0=Z01;
f1=1e+9;
f2=2e+9;
w1=2*pi*f1;
w2=2*pi*f2;
syms w  
beta=w/v;
a1 = z(1);
a2 = z(2);
a3 = z(3);
% ABCD Matrix
for m=1:1:section
    l=m*a;
    Z0=a0+(a1*l)+(a2*(l^2))+(a3*(l^3));
    B(m)=1i*Z0*sin(beta*a);
    C(m)=1i*(1/Z0)*sin(beta*a);
end
Bsum=sum(B);
Csum=sum(C);
ABCD=[1 Bsum ; Csum 1];
% Convert into S11
S11=((ABCD(1,2)-ABCD(2,1)*Z01*Z02)+((ABCD(1,1)*Z02)-(ABCD(2,2)*Z01)))/((ABCD(1,2)+ABCD(2,1)*Z01*Z02)+((ABCD(1,1)*Z02)+(ABCD(2,2)*Z01)));
gamma=abs(S11);
% Optimize objective
y1=subs(gamma,w,w1);
y2=subs(gamma,w,((w1+w2)/2));
y3=subs(gamma,w,w2);
% Converting to double after the fact is simpler to type for this example
% than removing all your vpa and sym calls, but for your real code I'd
% perform the removal to avoid involving Symbolic Math Toolbox at all
y1 = double(y1);
y2 = double(y2);
y3 = double(y3);
Y = (1-y1)+(1-y3)+(y2);
end
function [c,ceq] = constraintFcn_new(z)
% Reuse rather than duplicating
[Y, y1, y2, y3] = optfun(z);
fprintf("  Y is %g\n y1 is %g\n y2 is %g\n y3 is %g\n", Y, y1, y2, y3)
fprintf("check: %g\n", (1-y1)+(1-y3)+y2)
y1 = z(1);
y2 = z(2);
y3 = z(3);
c(1) = -y1+0.9;
c(2) = y2-0.1;
c(3) = -y3+0.9;
c(4) = y1-1;
c(5) = -y2;
c(6) = y3-1;
ceq=[];
end

Steven Lord 2023-8-24

在 MATLAB Online 中打开

You're calling the optfun to generate the intermediate values of your objective function, then after the fprintf lines (which I added just to show you that the constraint function had correctly obtained the values from the objective function) you throw away those intermediate values and replace them with elements of the input with which fmincon called the constraint function. Don't do that. Delete these lines from your constraint function: