Optimize Function with two sums using fmincon

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

Answer 1

[Matt J]

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

[Meikel Vollmers]

Thanks for the answer, but i think theres still a little mistake. Just for understanding: d is the distortion factor of a sinusoidal wave. k is the harmonic order.

p is the amount of commutation angles over one period in my Inverter, and i want to know for which angles d is minimized.

When i reduce the number of harmonics to be eliminated, i.e. i want to minimize the THD of the 5,7 and 11th harmonic order (so k= [5,7,11]), and i want to to this with at least 6 commutation angles (p=6), this isnt possible because of the matrix dimensions. So in my understanding the code works wrong because he reduces the function when k = 5 only for p=1, when k=7 only for p=2 and so on, requested is a reduction for k = 5 with p=1:6 and for k=7 with p=1:6 also.

I was searching for the right word. What i need is that the code respects the principle of nested sums.

[Matt J]

Small fix:

fun = @(a)  sum(   weights(:).*(  1 + 2*sum(  (-1).^p.*cos(k(:).*a) ,2)    ).^2  );

[Meikel Vollmers]

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?

[Matt J]

It needs to be,

nlcon = @(a) modindex(a,p);