变分法应用条件的探索及其灵敏度分析

The Exploration of the Condition of Variation Method and Sensitivity Analysis

考虑和探究变分法中的各种条件,通过对极值必要条件的探索和对不固定的自然条件的端点进行分类讨论,以及对横截性条件的端点问题进行探究,最终得到对变分法应用条件的总结以及各种情形的分析讨论,使得变分法可以更好地拓展和运用到许多实际问题中.在此基础上对变分法的各类讨论情形进行了灵敏度分析,考察当参数变化时,原目标函数的最优解变化情况,以及变化率的高低,推导并得出可直接求变分法的灵敏度的公式.由此简化了获取灵敏度的难度,及复杂性,并将所得的灵敏度公式应用于实践.

The various conditions of variational method was explored through the exploration of necessary conditions of ex-treme and classified discussion on the endpoints of unfixed natural conditions. Endpoint issues of transversality condi-tions were explored so as to eventually get the summary of application conditions of variational method, ensuring the bet-ter development and further application of variational method in solving practical problems. Sensitivity analysis were thencarried out on the basis of the above research of variational method to observe the shift of optimal solution of original ob-jective function with parameters change, as well as the rate of change. And a formula of directly getting the sensitivity rateof variational method were derived. This simplifies complexity in accessing sensitivity issues.