对变分问题的灵密度分析

Sensitivity analysis in problem of variations

考虑变分问题的灵密度分析,利用扰动法推出边界值问题和流动方程,以此来获得偏导数(灵敏性)的目标函数的所有参数。主要考虑参数系变分问题的灵密度分析,当参数产生改变时,它相应的最优解是如何随之而改变的,为了问题简单,开始考虑有限维参数的变分问题,最后定理4给出灵密度分析的一个固定公式,这个结果利于直接通过原始的目标函数关于参数P分析灵密度。

This paper deals with the problem of sensitivity analysis in calculus of variations. A perturbation technique is applied to derive the boundary value problem and the system of equations that allow us to obtain the partial derivatives （sensitivities） of the objective function value, we main consider a parametric family of variations problems and analyze how the corresponding optimal solutions change when parameters are modified. For the sake of simplicity, we start with considering the case of finite parameters. The practical consequences of theorem are the direct formulas for the sensitivities.