混合整数非线性规划问题的全局最优性条件（英文）  

Global optimality conditions for mixed integer nonlinear programming problems

作　　者：全靖[1] 李国权[2] 

机构地区：[1]宜宾学院数学学院,宜宾644000 [2]重庆师范大学数学科学学院,重庆401331

出　　处：《四川大学学报（自然科学版）》2017年第3期452-458,共7页Journal of Sichuan University(Natural Science Edition)

基　　金：四川省教育厅重点项目基金(14ZA0270)

摘　　要：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,该问题包含连续优化问题和离散优化问题为特殊情形,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,其中规划问题的目标函数只需要二次连续可微.如果目标函数是二次的,则所得的全局最优性条件易于验证.数值例子说明了全局最优性条件的意义.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 are 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.

关 键 词：全局最优性条件 混合整数非线性规划问题 界约束 

分 类 号：O221.2[理学—运筹学与控制论]