Model description
We have a non-linear mathematical model with the following set, variables, and parameters:
Set t in [1,N_T]
| Variables x_t y
| Parameters A B C_t |
And the following objective function:
min{sum((x_t-A)/A) for all t}
Subject to:
x_t = x_{t-1} + B(Ay - x_{t-1}y - C_{t-1})
x_t >= 0
1<= y <= 2499999
With the initial value of the variable x_t being:
x_1 = 19,500
The values of the set are:
t = >1 2 3 4 5 6 7 8 9 10]
The values of the parameters are:
A = 21,500
B = 0.00095
C_t = _50,000 50,240 50,300 51,000 51,040 50,700 50,800 50,200 49,000 48,700]
Solving
The non-linearity in the problem lies in the following product in the constraint:
x_{t-1}y
We have implemented the model in AIMMS and tried the Outer Approximation algorithm for this problem, but get the following error message:
The generated mathematical program “OA_NLP” has type “QCP” which cannot be changed into “RMINLP”.
What might be causing this message?
Also, does anyone have suggestions on other ways to solve this model, for example ways to linearise it?