Optimize Function with two sums using fmincon

Question

Meikel Vollmers 2021-5-11

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/827440-optimize-function-with-two-sums-using-fmincon

编辑： Matt J 2021-5-17

采纳的回答： Matt J

在 MATLAB Online 中打开

Hey everybody,

i have to calculate the a(i) to optimize the following function

k = [5,7,11,13]

p = [1:6]

the a(i) have to be between [0,pi/4]. I want to use the fmincon function, but i dont know how to programm the function d. My first try was the following:

k = [5,7,11,13];
p = [1:4];
a0 = [pi/10, pi/8, pi/7, pi/5];
f1 = sum(1./k.^4)*(1.+2.*sum((-1).^p.*cos(k.*a(p)))).^2;
f2 = sum(1./k.^4);
obj = sqrt(f1./f2);
A = [];
B = [];
Aeq = [];
Beq = [];
lb = [0,0,0,0];
ub = [pi/4,pi/4,pi/4,pi/4];
x = fmincon(Sum, a0, A, B, Aeq, Beq, lb, ub);

But this is not working at all. "Error using optimfcnchk (line 117) FUN must be a function, a valid character vector expression, or an inline function object."

Furthermore the code does not provide an overall combination of the parameters, so i tried it this way

Sum = 0;    
a = [pi/8, pi/7, pi/6, pi/5];
    for k = [5,7,11]
        for p = [1:4]
     Sum = Sum + sqrt(((1/k.^4) * (1+2*(-1).^p .*cos(k*a(p)).^2) / (1/k^4)));
     
    end
    end 
A = [];
B = [];
Aeq = [];
Beq = [];
lb = [0,0,0,0];
ub = [pi/4,pi/4,pi/4,pi/4];
x = fmincon(Sum, a, A, B, Aeq, Beq, lb, ub);

But now the function cant be used in fmincon.

Can somebody help me how i can implement the desired funnktion to be optimized with fmincon?

Regards

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Answer 1

Matt J 2021-5-11

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/827440-optimize-function-with-two-sums-using-fmincon#answer_697615

编辑：Matt J 2021-5-12

在 MATLAB Online 中打开

k = [5,7,11,13];
p = [1:4];
a0 = [pi/10, pi/8, pi/7, pi/5];
weights=(1./k.^4);
weights=weights/sum(weights);
fun = @(a)  sum(   weights(:).*(  1 + 2*sum(  (-1).^p.*cos(k(:).*a) ,2)    ).^2  );
A = [];
B = [];
Aeq = [];
Beq = [];
lb = [0,0,0,0];
ub = [pi/4,pi/4,pi/4,pi/4];
x = fmincon(fun, a0, A, B, Aeq, Beq, lb, ub)
Local minimum found that satisfies the constraints.

Optimization completed because the objective function is non-decreasing in 
feasible directions, to within the value of the optimality tolerance,
and constraints are satisfied to within the value of the constraint tolerance.
x = 1×4
    0.1841    0.2809    0.5394    0.5736

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Meikel Vollmers 2021-5-17

在 MATLAB Online 中打开

Hey Matt, the fix seems to be working. Now i want to implement a constraint into my function.

and m will be chosen to i.e. 0.7.

I tried the nonlinear constraint this way:

function [c,ceq] = modindex(a,p)
c = [];
ceq = 4/pi.*( 1 + 2*sum( (-1).^p.*cos(a(p)) ,2 ))-0.7;
end
nlcon = @modindex;
x = fmincon(fun, a0, A, B, Aeq, Beq, lb, ub, nlcon)

But the error is "Not enough input arguments." What am i doing wrong?