TOMLAB /MINLP
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.
Features and capabilities

The solver
MINLP_{bb} solves large, sparse or dense
mixedinteger linear, quadratic and nonlinear programming problems.
MINLP implements a branchandbound algorithm searching a tree whose nodes
correspond to continuous nonlinearly constrained optimization problems.
The continuous problems are solved using filterSQP,
see below.

The filterSQP solver is a Sequential Quadratic Programming solver
suitable for solving large, sparse or dense linear,
quadratic and nonlinear programming problems.
The method avoids the use of penalty functions.
Global convergence is enforced through the use of a trustregion and the
new concept of a filter which accepts a trial point whenever the
objective or the constraint violation is improved compared to all
previous iterates. The size of the trustregion is reduced if the step
is rejected and increased if it is accepted, provided the agreement between the quadratic model and the nonlinear
functions is sufficiently good.

The solver
MIQP_{bb}
solves sparse and dense mixedinteger linear and
quadratic programs.

The BQPD code
solves quadratic programming (minimization of a quadratic function
subject to linear constraints) and linear programming problems. If the
Hessian matrix Q is positive definite, then a global solution is found.
A global solution is also found in the case of linear programming (Q=0).
When Q is indefinite, a KuhnTucker point that is usually a local solution is found.
The code implements a nullspace active set method with a technique for
resolving degeneracy that guarantees that cycling does not occur even when
roundoff errors are present. Feasibility is obtained by minimizing a sum
of constraint violations. The Devex method for avoiding nearzero 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.

TOMLAB /MINLP is integrated with the TOMLAB optimization environment.

The TOMLAB /MINLP solvers may be used as subproblem solvers in the TOMLAB
environment.
Requirements
