MISQP: A Fortran Subroutine of a Trust Region SQP Algorithm for Mixed-Integer Nonlinear Programming

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 inor decrementing an integer value, successive quadratic approximations are applied. The algorithm is stabilized by a trust region method including Yuan’s second order corrections. It is not assumed that integer variables are relaxable. In other words, problem functions are evaluated only at integer points. The Hessian of the Lagrangian function is approximated by BFGS updates subject to the continuous and integer variables. The usage of the code is documented and illustrated by an example.