摘要
建立了一类具广泛应用价值的物体运动非线性泛函优化模型,包括目标泛函,决策函数,约束条件,可行函数空间.决策函数是能量消耗分配函数,可行函数空间中的能量消耗分配函数确定目标泛函值,该模型的最优解是使目标泛函值最大的能量分配函数.这个非线性泛函优化模型,表述了一类物体运动能量转化为机械功的实际问题.例如机动车行驶中如何控制燃料消耗方式,使燃油消耗最少.运动员在赛跑中如何分配体能消耗使成绩最好等.该文从非线性泛函变分及优化理论角度对该模型进行了定量探讨.所得结果可应用于物体运动功能转化相关实际问题中.该文也提出了若干公开问题.
The article will establish a nonlinear functional optimizing model of motion of substance which is constituted by objective functional, decision function, constraint condition and feasihle space of function. The decision function, that is expressed the speed of distribute of energy. This nonlinear＇functional optimizing model will express a kind of problem which about the transfrom energy into mechanical work of motion of substance. This article will give several results about optimal solution and applications by using variational method. The article will also advance some open problems.
出处
《大学数学》
北大核心
2008年第2期94-99,共6页
College Mathematics
基金
天津市学科建设基金项目(100580204)
关键词
泛函模型
最优化
能量分配函数
最优解
应用
functional model
optimization
optimal solution
motion Of substance
applications
