TOMLAB /MINLP provides an advanced Matlab solution which includes four solvers developed by Roger Fletcher and Sven Leyffer at the University of Dundee. The solvers have been compiled in both a sparse and a dense version.
The code implements a null-space active set method with a technique for
resolving degeneracy that guarantees that cycling does not occur even when
round-off errors are present. Feasibility is obtained by minimizing a sum
of constraint violations. The Devex method for avoiding near-zero pivots is
used to promote stability. The matrix algebra is implemented so that the
algorithm can take advantage of sparse factors of the basis matrix.
Factors of the reduced Hessian matrix are stored in a dense format,
an approach that is most effective when the number of free variables
is relatively small. The user must supply a subroutine to evaluate the
Hessian matrix Q, so that sparsity in Q can be exploited.
An extreme case occurs when Q=0 and the QP reduces to a linear program.
The code is written to take maximum advantage of this situation,
so that it also provides an efficient method for linear programming.
MATLAB 6.5 or later