## MISQP: A Fortran Implementation of a Trust Region SQP
Algorithm for Mixed-Integer Nonlinear Programming - User's Guide

O. Exler,
T. Lehmann, K. Schittkowski, Report, Department of Computer Science, University of Bayreuth
(2012)

**Abstract:**
The Fortran subroutine MISQP solves mixed-integer nonlinear programming
problems by a modified sequential quadratic programming (SQP) method. Under the
assumption that integer variables have a *smooth* influence on the model
functions, i.e., that function values do not change drastically when in- or
decrementing an integer
value, successive quadratic approximations are applied. The algorithm is
stabilized by a trust region method with Yuan's second order corrections. It is
not assumed that the mixed-integer program is relaxable. In other words,
function values are evaluated only at integer points. The Hessian of the
Lagrangian function is approximated by BFGS updates subject to the continuous
and integer variables. Numerical results are presented for the continuous case
to compare the performance with a standard SQP solver, and for a set of 80
mixed-integer test problems taken from the literature. The surprising result is
that the number of function evaluations, the most important performance
criterion in practice, is less than the number of function calls needed for
solving the corresponding relaxed problem without integer variables. The usage
of the code is documented and illustrated by an example.

To download the report, click here: MISQP.pdf