For loops in non linear equaities - fmincon

Hi

I wanna use a for loop in the non linear equity for the fmincon. I wanna minimize variable x(1) and yet even when a solution is posible, the exitflag is sometimes -1. Why cant i use a for loop in a non linear equity for the fmincon?

Here is a simplified version of my code:

function [c,ceq] = nonlconTest(x)
n = x(1);
P = x(2)

T = zeros(50,1) + 200
T(1) = 20

for i = 1:n
   E(i) = -86.095*T(i) + 200471;
   ang(i) = P *E(i)
end

c = [];
ceq = [sum(ang) - 10];
end

Answer 1

[Walter Roberson]

function [c,ceq] = nonlconTest(x)
n = x(1);

That tells us that n is one of the variables being allowed to vary.

for i = 1:n

That is a calculation that is discrete in n and so is discrete in the first variable x(1) . However, fmincon() requires the functions to be continuous in the inputs.

Exception: if you had set upper bound and lower bound to be identical for the first variable, then fmincon would be okay with that.

[Walter Roberson]

T = zeros(50,1) + 200
T(1) = 20
for i = 1:n
   E(i) = -86.095*T(i) + 200471;
   ang(i) = P *E(i)
end

So T(1) is 20 and the rest of T are 200.

You are doing n iterations. For the first one, T(1) is 20, and you caculate

E(1) = -86.095*20 + 200471

for the rest, E(2:n) you calculate

-86.095*200 + 200471

You calculate ang as P*E(i) . But P is constant relative to that, so when you calculate sum(ang) you have sum(P*E(1) + P*E(2) + ... P*E(end)) which is P * sum(E(1) + E(2) + ... E(end))

So what is the sum? It is going to be

-86.095*20
+ 200471
-86.095*200 * (n-1)
+ 200471

which will be

-86.095*(200*n-200+20) + 200471 * n

which is

-86.095*200*n + 200471 * n + 180*86.095

which is

(200471-17219)*n + 15497.1

That is then being multiplied by P, and the result must equal 10 because this is an equality constraint.

What value of n satisfies that?

[Walter Roberson]

syms n
solve( (200471-17219)*n + 15497.1 == 10)

ans = 

vpa(ans)

ans = 

You need a negative x(1) for that to hold. But a negative x(1) would cause the code to fail with ang never have been assigned to.

So, what you are asking for is not possible.