一类取整函数的极小值问题研究

The minimal value issue of a class of integral functions

取整函数经常出现在组合优化问题的模型中。由于求极值的困难性,制约了其实际应用。为解决这一难题,文中提出两类常用取整函数的极小值问题,并用微分与差分的方法求得它们的极小值点与极小值。使用的方法和结论具有一般性,对求其他类型的取整函数极值问题具有积极作用。

The integral fuctions often appear in the models of optimization issues.Howerer,because of the solving complexity,their applications are constrained to a certain extent.For the sake of solving the problem,this paper puts forwaods two types of integral functions and gives the minimal points and values by the method of differential and differerce.The method and conclusion in this paper have a general significance,so it can be applied to solve other extreme integral function problems.