We propose a modified sequential quadratic programming (SQP) method for solving mixed-integer nonlinear programming problems. 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 can be evaluated only at integer points. The Hessian of the Lagrangian function is approximated by BFGS updates subject to the continuous and diagonal second order information subject to the integer variables. Numerical results are presented for a set of 80 mixed integer test problems taken from the literature.

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