一类混合整数约束三次规划问题的全局最优性条件

Global Optimality Conditions for Mixed Integer Cubic Programming Problems

通过构造目标函数的二次上估计函数和二次下估计函数,给出了一类混合整数三次规划问题的全局最优性条件。首先利用二次上估计函数给出全局最优性必要条件,其次再利用二次下估计函数获得全局最优性充分条件。最后给出一个数值例子来说明如何利用所给出的全局最优性条件来判定一个给定的点是否是全局最优解。

In this paper,we establish some necessary and sufficient global optimality conditions for mixed integer cubic programming problems via quadratic overestimators and underestimators.Firstly,by utilizing quadratic overestimators,we derive some necessary global optimality conditions for mixed integer cubic minimization problems where the cubic objective function contains no cross terms.Then,we obtain some sufficient conditions for global minimizers using quadratic underestimators.Finally,an example is given to illustrate how to use the global optimality conditions to check a given point.