一般多阶段有补偿问题的间接单阶段化及其应用

Indirect One Staging of General Multistage Problem with Recourse and Its Application

对陈志平在１９９２年博士学位论文中所讨论的一般多阶段有补偿问题，通过引进松弛函数，给出了一个恰当，合理的，其目标函数与约束函数均不太复杂的单阶段化问题，并论证了二者之间的等价性，从而克服了已有单阶段化方法的缺点。在讨论上述结果的应用中，特别是利用已有半无限规划算法导出了求解一般非线性多阶段有补偿问题的积分罚函数法，为求解该类问题提供了一种新的途径。

Abstract For the general multistage problem with recourse discussed in paper , we derive a proper, reasonable one staging problem with unsophisticated objective function and constraint functions through introducing slack functions, prove the equivalence between them, thus overcome the disadvantages of available one staging methods. then we discuss the application of above results. Whats more important is that an integral penalty function method is derived by utilizing the existing relevant semi infinite programming algorithms, which provide a new way to solve this kind of complex problem.