双值约束三次规划问题的全局最优性充分条件

Sufficient Global Optimality Conditions for a Special Cubic Minimization Problem with Bivalent Constraints

利用拉格朗日函数L-次微分的方法,给出了双值约束的三次极小化问题的全局最优性充分条件,而且得到了此类三次规划问题在一些特殊情况下的结果,与已有文献中的相应结论是一致的;同时给出例子说明给出的最优性条件能有效用于确定给定的三次极小化问题的全局极小值;所得结果改进和推广了相关文献中的相应结果.

By using Lagrangian function and subdifferential approach,this paper presents some sufficient global optimality conditions for a cubic programming problem with binary constraints,and in some special cases,the results obtained in this paper are equivalent to some corresponding results in reference [9]. An example is given to demonstrate that the optimality conditions can effectively be applied to identifying global minimizers of the certain noncovex cubic minimization problem. The results improve and generalize the corresponding ones in the reference [9].