求解非线性规划问题的两个微分方程系统(英文)  

Two Differential Systems for Solving Nonlinear Programming Problems

作　　者：张立卫[1,2] 张立卫[1,2] 李勤[2] 张鑫 

机构地区：[1]中国科学院计算数学研究所,北京100080 [2]大连理工大学应用数学系,大连116024

出　　处：《运筹学学报》2000年第4期33-46,共14页Operations Research Transactions

基　　金：Supported by the Natural Science Youth Foundation of China.

摘　　要：本文给出 Ｅｖｔｕｓｈｅｎｋｏ与Ｚｈａｄａｎ（ １９７４）提出的求解数学规划问题微分方程系统的两个校正形式，它们可用于求解具有等式和不等式约束的非线性规化问题．第一个校正系统拓宽了Ｅｖｔｕｓｈｅｎｋｏ与Ｚｈａｄａｎ 微分方程方法；第二个校正系统通过引入新的方程系统导出乘子函数得到，它无需使用Ｅｖｔｕｓｈｅｎｋｏ与Ｚｈａｄａｎ所用的那样强的约束规范．我们建立了这两个微分方程方法及其离散迭代方法的收敛性定理，给出了基于第二个微分方程离散格式的数值算法及其某些数值结果．This paper presents two modified versions to the differential system proposed by Evtushenko and Zhadan (1974), for solving mathematical programming problems. Both modified systems may be used to solve nonlinear optimization problems with both equality and inequality constraints. The first version extends the range of differential equation methods given by Evtushenko and Zhadan. A new system is introduced for deriving multiplier functions in the second version, which enables it use a less restrictive constraint qualification than that used by Evtushenko and Zhadan (1994). The convergence theorems for both the modified differential systems and their discrete schemes are established. An algorithm, based on the discrete approach of the second version, is given and some numerical experiments are described.

关 键 词：非线性规划 约束规范 微分方程 平衡解 数值算法 离散格式 

分 类 号：O221.2[理学—运筹学与控制论] O241.8[理学—数学]