The Quesada-Grossmann Algorithm
One MIP problem
Quesada and Grossmann ([QG92]) noticed that the classic outer approximation algorithm often spends a large amount of time in solving the MIP problems in which a significant amount of rework is done. They proposed an algorithm in which only one MIP problem is solved. The algorithm implemented in AIMMS uses a callback procedure for lazy constraints which is supported by modern MIP solvers like CPLEX and Gurobi.
The Quesada-Grossmann algorithm is designed to solve convex MINLP
models. The basic outer approximation algorithm can also be used to
solve convex models by using the parameter
IsConvex, but the
Quesada-Grossmann algorithm is often more efficient. The
Quesada-Grossmann algorithm is also available in the
GMP Outer Approximation module.
DoConvexOuterApproximation inside the module
implements the Quesada-Grossmann algorithm. This procedure is called in
the same way as the
DoOuterApproximation procedure of
Using the AOA Algorithm, which implements the basic algorithm.
The following control parameters in this table can
be used to influence the Quesada-Grossmann algorithm: