I have a function that cannot be maximized by taking the FOCs, i.e. non-convex, and I want to maximize it with respect to two variables. Say, with respect to (x,y).
I have found an example where you can extract the maximizer from plot using this approach:
MAX := 0.330385487730942451
MAXPT := [[0.287405284999999956, 0.330385487730942451]]
The above example is for the case where you maximize a function with respect to a single variable, y. (The value of x is fixed above; tau, theta, and omega are parameters of payoff.)
I would like to use a similar approach with plot3d to find the maximizer of the payoff function with respect to (x,y).
I tried the following:
P3 := INTERFACE_PLOT3D(GRID(0. .. 1., 0. .. 1., Array( 1..25,1..25,[ ... ], [ ... ], datatype = float, storage = rectangular, order = Fortran_order )), AXESLABELS(s, p, ""))
MAX3 := 2
points3 := 0. .. 1.
MAXPT3 := ..
but it returns an empty expression. I think that the problem lies with the way I am defining "points3" above. How do I extract the set of points from the plot3d function, using op, so that I can look for a maximizer in this set of points (which will actually be triples, right? (x,y,payoff_value)