求解半无限规划问题的一类新的精确罚函数方法
A New Exact Penalty Function Method for Solving Semi-Infinite Programming Problems
DOI: 10.12677/ORF.2017.74014, PDF,   
作者: 张艳萍, 刘 茜：山东师范大学数学与统计学院，山东 济南
关键词: 半无限规划；精确罚函数；罚函数算法；Semi-Infinite Programming； Exact Penalty Function； Penalty Function Algorithm
摘要: 对于半无限规划问题，我们提供了一种新的概括性的精确罚函数，它包含了许多常用的罚函数作为特例。我们证明了在适当的约束规格条件下，当罚参数充分大的时候，罚问题的局部最优解也是原问题的局部最优解。另外，在适当的条件下我们证明了罚问题的全局最优解序列收敛于原问题的全局最优解。
Abstract: For semi-infinite programming problems, we provide a new generalized exact penalty function, which contains many commonly used penalty functions as a special case. It is proved that the local optimal solution of the unconstrained optimization subproblem is also the local optimal solution of the original problem when the penalty parameter is sufficiently large under some constraint qualification. Moreover, under suitable conditions, we also prove that the global optimal solution sequence of unconstrained optimization subproblem converges to the global optimal solution of the original problem.
文章引用：张艳萍, 刘茜. 求解半无限规划问题的一类新的精确罚函数方法[J]. 运筹与模糊学, 2017, 7(4): 138-147. https://doi.org/10.12677/ORF.2017.74014

参考文献

[1] Polak, E. and Mayne, D.Q. (1976) An Algorithm for Optimization Problems with Functional Inequality Constraints. IEEE Transactions on Automatic Control, 21, 184-193. [Google Scholar] [CrossRef] 
[2] Polak, E., Mayne, D.Q. and Stimler, D.M. (1984) Control System Design via Semi-Infinite Optimization: A Review. Proceedings of the IEEE, 72, 1777-1794. [Google Scholar] [CrossRef] 
[3] Jennings, L.S. and Teo, K.L. (1990) A Computational Algorithm for Functional Inequality Constrained Optimization Problems. Automatica, 26, 371-375. [Google Scholar] [CrossRef] 
[4] Teo, K.L., Rehbock, V. and Jennings, L.S. (1993) A New Computational Algorithm for Functional Inequality Constrained Optimization Problems. Automatica, 29, 789-792. [Google Scholar] [CrossRef] 
[5] Teo, K.L., Yang, X. and Jennings, L.S. (2000) Computational Discretization Algorithms for Functional In-Equality Constrained Optimization. Annals of Operations Research, 98, 215-234. [Google Scholar] [CrossRef] 
[6] Yang, X. and Teo, K.L. (2001) Nonlinear Lagrangian Functions and Applications to Semi-Infinite Programs. Annals of Operations Research, 103, 235-250. [Google Scholar] [CrossRef] 
[7] Ito, S., Liu, Y. and Teo, K.L. (2000) A Dual Parametrization Method for Convex Semi-Infinite Programming. Annals of Operations Research, 98, 189-213. [Google Scholar] [CrossRef] 
[8] Liu, Y., Teo, K.L. and Wu, S.Y. (2004) A New Quadratic Semi-Infinite Programming Algorithm Based on Dual Parametric. Journal of Global Optimization, 29, 401-413. [Google Scholar] [CrossRef] 
[9] 徐光辉, 刘彦佩, 程侃. 运筹学基础手册[M]. 北京: 科学出版社, 1999.
[10] Zangwill, W.I. (1967) Non-Linear Programming via Penalty Function. Management Science, 13, 344-358. [Google Scholar] [CrossRef] 
[11] Fletcher, R. (1973) An Exact Penalty Function for Nonlinear Programming with Inequalities. Mathematical Programming, 5, 129-150. [Google Scholar] [CrossRef] 
[12] Huyer, W. and Neumaier, A. (2003) A New Exact Penalty Function. SIAM Journal on Optimization, 13, 1141-1158. [Google Scholar] [CrossRef] 
[13] Wang, C., Ma, C. and Zhou, J. (2014) A New Class of Exact Penalty Functions and Penalty Algorithms. Journal of Global Optimization, 58, 51-73. [Google Scholar] [CrossRef] 
[14] Yu, C., Teo, K.L., Zhang, L. and Bai, Y. (2012) The New Exact Penalty Function Method for Continuous Inequality Constrained Optimization Problem. Journal of Industrial and Management Optimization, 8, 485-491. [Google Scholar] [CrossRef] 
[15] Yu, C., Teo, K.L, Zhang, L. and Bai, Y. (2010) A New Exact Penalty Function Method for Continuous Inequality Constrained Optimization Problems. Journal of Industrial and Management Optimization, 6, 895-910. [Google Scholar] [CrossRef] 
[16] Yu, C., Teo, K.L. and Zhang, L. (2014) A New Exact Penalty Function Approach to Semi-infinite Programming Problem. Optimization in Science and Engineering, 583-596. [Google Scholar] [CrossRef] 

为你推荐