CODEWITHSUNDEEP
pythonmathematical-optimizationamplgams-math
adam
adam

Reputation: 685

ampl vs gams MINLP portfolio optimization syntax

I am looking for a MINLP optimizer to solve portfolio optimisation problem which minimizes x'.S.x where x is a vector S is a given matrix. There are integer constraints which x elements depend on ex; x[i] = g[i].K[i] where g[i] is an integer and K[i] is a given vector, thus we need to find g[i]s while minimizing objective.

I am considering using AMPL or gams. Main program is in python. I am not sure if these are the best MINLP out there, but anyways there seems to be some examples on both websites. In terms of matrix multiplication for the minimization objective, I am not clear if there is a simple way of writing this in AMPL, do I need to write it as an algebraic expansion? Can you provide an example of x'.S.x operation in AMPL language?

In terms of gams, I see the package is free only for limited usage of a number of variables. Therefore I was considering AMPL, but maybe for smaller problems gams might be the solution if I cannot figure out AMPL notation for matrix vector multiplications

Upvotes: 0

Views: 291

Answers (1)

Erwin Kalvelagen
Erwin Kalvelagen

Reputation: 16797

The AMPL syntax is very straightforward:

sum{i in I, j in I} x[i]*S[i,j]*x[j]

Note that many portfolio models do not need a full-blown MINLP solver but can be solved with the quadratic (and SOCP) capabilities present in systems like Cplex and Gurobi. Your question is somewhat difficult to parse (at least for me) but I believe your model falls in this category.

Upvotes: 0

Related Questions