In recent years, the application of mixed integer nonlinear programming problem has been extremely active and very extensive. In this paper, some necessary conditions for a given global minimizer applied to mixed integer nonlinear programming problem with bounded constraints which arises in continuous as well as discrete optimization have been developed. Also, some sufficient global optimality conditions for mixed integer nonlinear programming problem with bounded constraints are established. The global optimality conditions readily apply to problems whose objective functions are generally twice continuously differentiable. If the objective functions are quadratic, then the global optimality conditions become verifiable. Some simple numerical examples can illustrate the significance of the optimality conditions.
