I am solving a constrained maximization problem using the Lagrangian and getting back an empty set of solutions, i.e.:
How do I go about diagnosing why Maple is having difficulty finding solutions?
(Once I know that, I would of course also like to know how, if possible, to change the set-up so that Maple might actually find the solution(s)!)
I can see that the Lagrangian becomes non-concave for cases where lambda2>p (p is one of the variables I am solving for: there are two, s and p -- see attached worksheet).
This would clearly be the case for, say, p=0 optimal (which I have reason to believe it is, based on some numerical simulations I ran).
In fact, in the attached worksheet I plot the function I am maximizing and it looks as if the optimal solution is s=m and p=0, but Maple doesn't seem to find this.
Link to worksheet 'Example-Lagrangian:'