I am trying to solve an optimization problem where the given objective function is to minimize
norm(R - R*)
where R is obtained by solving a boundary value problem (BVP) and `R* is a known value.
For example:
R = (p1 + p2*p3);
The BVP is given by
p1dot = p2 + p3 + x1;
p2dot = x2 + p1*p2;
p3dot = x3 + p1*p2*p3;
where x1, x2 and x3 are the optimized variables.
I am trying to solve this in MATLAB using fmincon where the BVP is solved in the objective function at every guess by the solver to estimate norm(R-R*).
EDIT 1 : I have a non linear inequality constraint which is a function of pi where i = 1,2,3. This is the reason for choosing fmincon
The issue I am facing is that during some guesses the BVP doesn't converge and the optimization stops. I guess the issue is some guess value to solve the BVP doesn't satisfy. If I give bounds to the variables then it solves the optimization problem. I am not really aware of the bounds on variables beforehand.
In order to overcome this I want to detect the guess when BVP is not solved, save them and force the optimization routine to not try values when it cannot be solved by going back to its previous guess. How do we implement this in fmincon routine?
EDIT 2 : I figured out the issue is with initial guess provided to the BVP solver. For smaller values of the optimization variables x this guess is good but when the magnitude of x increase this guess is not good enough.
Is there a way to update the solution of 'BVP' in the previous iteration as the initial guess for the next iteration in optimization. Intuitively this should fix it. Please let me know if there are some loop holes in this method.