I have an optimization problem which I can explain in words; but I am attempting to define it mathematically to make it more easily understood (by those who know math better than I).
I have a function which determines how much experience is required to reach the next level:
To_Reach_Next_Level = floor(To_Reach_Next_Level(Current_Level-1) * 1.01) where Level_0 = 500
another function which determines the amount of experience given (and includes a reference to the previous function):
Experience_Gained = To_Reach_Next_Level(Current_Level+1) * G * (1.0 - (Current_Level - J) / K)
G, J, and K all come from sets of numbers similar to:
{ { G=0.3, J=1, K=25 }, { G=0.6, J=5, K=50 } }
This set of numbers is much longer than just 2 points - somewhere between 40-100. Each "point" has an inherent "cost" which is 0 or greater. These points and cost are the "unknown" of the equation - and differ from one problem to the next.
My goal is to find a set of points from those given that minimizes cost while gaining enough experience to reach Level 400. Note that the same point can be applied multiple times.
there are a set of constraints, which I'm not sure whether they can affect the optimization or not:
1.0 <= Current_Level <= 400
1.0 <= J <= Current_Level
0.3 <= L <= 1.85
25 <= K <= 250
The example:
At level 0, it requires 500 experience to reach level 1.
At level 1, it requires 505 experience to reach level 2 (Experience at level 0 * 1.01)...
At level 59, it requires 864 experience to reach level 60.
The experience given from point { G=0.6, J=50, K=25 } where Current_Level is 59 is...
Exp_Gained = To_Reach_Next_Level(Current_Level+1) * G * (1.0 - (Current_Level - J) / K)
Exp_Gained = 864 * 0.6 * (1.0 - (59-50)/25) = 332
My primary question: How do I restate this problem in a more mathematically concise and clear way?