I have a two stage stochastic programming model which uses a quadratic utility function of the form -(1/b)*(X-b)^2 as the objective to be maximized. Here X represents the return of each scenario.
To implement this, I have declared a variable u_s and added the quadratic constraints:
for s in S: u_s <= gp.QuadExpr(-(1/b)*gp.QuadExpr((x_s-b)*(x_s-b))
The objective function is then the expectation over the utility in each scenario.
Running this model for different values of b I find that some outcomes are "optimal" while most terminate with sub-optimality (status 13).
My questions are:
- Why is this the case? How is this being solved?
- Can I control whether it becomes optimal or not?
- How can I determine the degree of sub-optimality?
Thank you in advance!
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