MISQPOA solves mixed-integer nonlinear problems by the modified sequential quadratic programming code MISQP stabilized by an outer approximation master program. Convergence can be guaranteed for convex programs. Outer approximation methods apply linear approximations at previous iterates to stabilize the algorithm and to guarantee global optimlity for convex problems. A mixed-integer linear programming master program must be solved to determine a lower bound. Afterwards, a nonlinear optimization program is generated to improve the best known point by solving another mixed-integer nonlinear program by the code MISQP. Additional safeguards allow to apply MISQPOA also to non-convex and non-relaxable nonlinear mixed-integer programs, but without guaranteeing global optimality. In the non-relaxable case, derivatives are approximated at neighbored grid points. MISQPOA is a FORTRAN subroutine where all data are passed by subroutine arguments. The generated subproblems are solved by MISQP.