MATLAB: How to use numerical fmincon

fminconoptimization

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?

Best Answer

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.
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