Can AMPL be used to solve SOCP

Question

In this link,http://mosek.com/products/ampl/ it says ampl does not support conic problem. But it does not have details explanation. Could any help explain why ampl cannot solve conic problem ? Thanks,

Answer 1

AMPL does support conic programming when used with the CPLEX and Gurobi solvers. See for example these slides:

http://www.ampl.com/MEETINGS/TALKS/2012_08_Berlin_Thu.1.H1058.pdf http://www.ampl.com/MEETINGS/TALKS/2013_08_Lisbon_Thu.A.23.pdf

In brief, conic constraints are represented in AMPL as quadratic constraints, with a sum of squares of variables on the left-hand side, and either the square of a nonnegative variable or the product of two nonnegative variables on the right-hand side. Actually it is a little more general, as any term may be multiplied by a positive constant.

Answer 2

AMPL doesn't and cannot solve anything.

AMPL is a modeling environment (provided by AMPL Optimization LLC). It transforms your model into a form that can be passed on to another third party program called solver. The solver then solves your problem.

As others have already pointed out, AMPL is capable of representing conic problems. The solver provided by MOSEK ApS would be able to solve conic problems, apparently there is some problem in passing your model from the AMPL environment to the MOSEK solver.