• 论文 •

### 一个求解约束非线性优化问题的微分方程方法

1. 大连理工大学应用数学系,浙江海洋学院数理与信息学院 浙江舟山 316004,大连理工大学应用数学系,大连理工大学应用数学系,,辽宁大连 116024,辽宁大连 116024,辽宁大连 116024
• 出版日期:2007-02-14 发布日期:2007-02-14

### A DIFFERENTIAL EQUATION METHOD FOR SOLVING NONLINEARLY CONSTRAINED OPTIMIZATION PROBLEMS

1. Jin Li (Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, Liaoning, China; School of Mathematics, Physics and Information Science, Zhejiang Ocean University, Zhoushan 316004, Zhejiang, China) Zhang Liwei Xiao Xiantao (Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, Liaoning, China)
• Online:2007-02-14 Published:2007-02-14

The differential equation method in this paper consists of two differential equation systems, in which the first one is based on the first order information on problem functions and the second system is based on the second order information. These two systems possess the properties that the local minimum point is their asymptotically stable equilibrium point and the whole solution trajectories are in the feasible region of the problem if they start from initial feasible points. We prove the convergence theorems for their discrete schemes and the locally quadratic convergence property for the discrete method based on the second differential equation system. We give numerical examples based on these two discrete methods and the numerical results show that the differential equation system based on the second information is faster than the first one.
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