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一类约束不可微优化问题的极大熵方法

唐焕文,张立卫,王雪华   

  1. 大连理工大学应用数学系 ,大连理工大学应用数学系 ,大连理工大学应用数学系
  • 出版日期:1993-03-14 发布日期:1993-03-14

唐焕文,张立卫,王雪华. 一类约束不可微优化问题的极大熵方法[J]. 计算数学, 1993, 15(3): 268-275.

A MAXIMUM ENTROPY METHOD FOR A SORT OF CONSTRAINED NONDIFFERENTIABLE OPTIMIZATION PROBLEMS

  1. Tang Huan-wen;Zhang Li-wei;Wang Xue-hua Department of Applied Mathematics, Dalian University of Technology
  • Online:1993-03-14 Published:1993-03-14
1.引言 用极大熵原理可以有效地处理某些优化问题,一般迭代2—6次即可达到工程要求的精度。本文给出一类约束不可微优化问题的两种极大熵方法,推广了[1,2]的结果,并研制了计算程序。试算结果说明效果良好。进一步的结果在[4]中给出。 考虑下述问题:
This paper presents a maximum entropy method for solving minimax problemswith inequality constraints, in which a multi-constrained minimax problem is appro-ximated by a differentiable one with a single constraint. An augmented Lagrangianalgorithm is used to solve the resulting problem. Numerical examples are given toshow the high efficiency of the method.
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[1] Li Xing-si (李兴斯) (1991) , An aggragate function method for nonlinear programming. Science in China (Series A), 34: 12(1991) , 1467-1473.
[2] 李兴斯.非线性极大极小问题的一个有效解法,科学通报,36:19(1991) ,1448-1451.
[3] 唐焕文,实用数学规划导论,大连工学院出版社,1986.
[4] Tang Huan-wen, Zhang Li-wei (1991) , A maximum entropy method for general differentiable constrained optimization problems and minimax problems, APORS'91 Beijing, China, 1991, 27-30.
[5] A. B. Templeman, Li Xing-si, A maximum entropy approach to constrained nonlinear programming, Eng. Opt. 12. 1987, 191-205.
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