混合整数非线性规划问题的全局最优性条件

近年来混合整数非线性规划问题的应用非常广泛。本文给出了带界约束的混合整数非线性规划问题全局极小点的必要条件，包含连续优化和离散优化问题。同时得到了带界约束的混合整数非线性规划问题的充分全局最优性条件。所针对的优化问题的目标函数只需要是二次连续可微的。如何目标函数的二次的，所得的最优性条件非常容易验证。我们给出了数值例子以说明全局最优性条件的意义。

Global optimality conditions for mixed integer nonlinear programming problems

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.