非线性管道网络中的数学规划问题及解法

MATHEMATICAL PROGRAMMING PROBLEMS IN NONLINEAR PIPELINE NETWORKS AND THEIR SOLUTIONS

非线性管网理论来源于矿井通风,城市给水,煤气供给和石油输送等一大类实际问题.这些实际背景不尽相同,但都可以通过增加虚拟分支和虚拟回路将它们等价于一个不含悬挂点的,具有相似特征的环流网络.自从出现 H.Cross 算法以来,无论是平差方程组的求解,还是设计与控制优化均取得了一些进展.但是,这些理论与算法只局限于某些特定的简单问题,在理论上还很不完善.如,关于平差方程组的研究,只有[2]、[3]给出了简单加压问题解的存在唯一性讨论和收敛算法.文[4—6]虽然也采用了最优化技术求解平差方程组也限于简单情况,且远不如[2,3]中的结果.而在实际问题中出现的大都是比简单加压问题复杂得多的控制问题.遗憾的是对控制方程组,只有[7]给出了一个有唯一解的必要条件,而这个条件一般不是充分的,而更实用的应是充分条件或充要条件.对于非线性管网的设计与控制优化问题,迄今。

This paper discusses the properties of a system of controlling equations of pipeline net-works,gives a new convex programming method to solve the system of equations with a uniquesolution,and proves the global convergence and the superlinear rate of convergence of the newmethod.Meanwhile,the paper also establishes a nonlinear programming model for solving theoptimization problem of the design and control of (?)he pipeline networks,presents a constrained(?)ariable metric algorithm,and proves the convergence of the algorithm under quite weak condi-tions.