How to use numerical fmincon

I have the following objective function

t = 0:0.01:1;
v = 3.*t;
objective =@(t) (1 - b).*( a1.*v + a2.*v.^2); %where a1,a2 given constants
S = sum(objectivet(t));
t0 = 1; 

But when applying the

 [t,fval,exitflag,output] = fmincon(S,t0,A,b,Aeq,beq,ub,lb,constraints)

it gives an error using fmincon.

All values using the fmincon are well defined. How could I correct it?

Answer 1

[Walter Roberson]

t = 0:0.01:1;

so t is a vector.

v = 3.*t;

So v is a vector the same size as t.

objective =@(t) (1 - b).*( a1.*v + a2.*v.^2); %where a1,a2 given constants

Assuming that a1, a2, and b are scalars. then this would take an input locally named t, ignore the input, and return a vector the same size as v, which is the length of the original t . fmincon does not expect that.

We might suspect that you perhaps want

t = 0:0.01:1;
v = @(T) 3.*T;
objective = @(T) (1 - b).*( a1.*v(T) + a2.*v(T).^2); %where a1,a2 given constants

Here I use T to distinguish the current parameter from the vector of length 101.

S = sum(objectivet(t));

We could suspect that objectivet is the same as objective . But as far as we know, objective takes only a single parameter, so objective(t) would be a definite vector and sum(objective(t)) would be a definite value, not something that could be optimized.

So the next suspicion is that you want

t = 0:0.01:1;
v = @(T) 3.*T;
objective = @(T, b) (1 - b).*( a1.*v(T) + a2.*v(T).^2); %where a1,a2 given constants
S = @(b) sum(objective(t, b));

and that is something that could reasonably be optimized.

It turns out that this can be optimized down to the expression

S = @(b) -(303*(b - 1)*(100*a1 + 201*a2))/200

and you can demonstrate easily that the minima of this is either at b = +inf or b = -inf or at one of the constraint boundaries.

[Thalassia Nouni]

Thank you, it works perfectly. How could someone see the optimized expression of an objective like you wrote in the last line?

[Walter Roberson]

syms B
simplify(S(B))