In my current mathematical inquiry, I would like to gain insight on behaviour of a $d$-dimensional continuous function by locating its maximum over the hyperplane $\sum_{i=1}^d x_i = 1$ for $x_i$ non-negative real.
Usually I'd attempt to either find the extreme using linear programming or Mathematica somehow, but in my current situation, both are impractical -- the function has no obvious symbolic form (it arises from game theory and is equivalent to evaluating a game tree of some depth) and the problem does not lend itself to linear programming because of its dynamic nature (evaluating minimax through LP is possible, but that usually means static payoff matrix, not a game that is played by selecting one point of a hyperplane).
Because of the nature of the game, for a given $d$-dimensional input, I can evaluate the function in quadratic time using dynamic programming methods.
I would like to find out what options do I have in terms of computer science/numerical tools for evaluating the maximum over the hyperplane for some small $d$, probably by trying to numerically find derivatives of said function.
(Note that I know I could employ LP with some trickery but that would lead to either inputs of exponential size of exponentially many variables and conditions, which goes against the fact that I can evaluate the function quickly, at a given point.)
I do admit that there may be a solution in Mathematica itself, I do not know its features that well. Thank you for any pointers.