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

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