You need two functions:
- Function to compute derivative. Mine is called "derivative."
- Function to compute objective function. Mine is called "objectiveFunction."
Once you have the objective function, call fmincon. I do this in runOptimization. Note that
a = 3.2737
b = 3.2530
runOptimization.m
ab0 = [1; 1]; % initial guess
A = [ 1 0; % a<100
-1 0; % a>0
0 1; % b<22
0 -1];% b>0
b = [100*(1-eps); % a<100
0-eps; % a>0
22*(1-eps); % b<22
0-eps]; % b>0
ab = fmincon(@objectiveFunction, ab0, A, b);
a = ab(1);
b = ab(2);
derivative.m
function df = derivative(x, f, ab)
a = ab(1);
b = ab(2);
df = zeros(3,1);
df(1)=3*a/b*f(2)*f(1)+16*(f(3)-f(1));
df(2)=-3*a/b*f(2)*f(1)+(f(3)-f(1));
df(3)= 5*a/b*f(1)+(f(2)+f(3));
end % end function, derivative
objectiveFunction.m
function cost = objectiveFunction(ab)
f0 = [1;1;1];
[~, f] = ode113(@(t,f) derivative(t, f, ab), [0 1], f0);
cost = f(2, end) + f(1, end) - 0.576;
end % end function, objectiveFunction
