# 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.

Convex models

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.

Calling procedure

The procedure `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: `TimeLimit`

,
`CreateStatusFile`

, `UsePresolver`

and
`RelativeOptimalityTolerance`

.