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研究生:李承翰
研究生(外文):Lee, Chen-Han
論文名稱:Some new types of the NCP-functions and their properties
論文名稱(外文):Some new types of the NCP-functions and their properties
指導教授:陳界山陳界山引用關係
指導教授(外文):Chen, Jein-Shan
學位類別:碩士
校院名稱:國立臺灣師範大學
系所名稱:數學系
學門:數學及統計學門
學類:數學學類
論文出版年:2021
畢業學年度:109
語文別:英文
論文頁數:27
中文關鍵詞:互補函數互補問題費雪-博美斯特函數
外文關鍵詞:NCP-functionNonlinear complementarity problemFischer-Burmeister function
相關次數:
  • 被引用被引用:0
  • 點閱點閱:17
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  • 下載下載:1
  • 收藏至我的研究室書目清單書目收藏:0
在這篇論文當中,我們觀察出一些互補函數是由可逆函數構造出來,像是有名的費雪-博美斯特函數。根據類似的結構,我們利用可逆函數 e^t 和 ln⁡t發現了其他兩個互補函數。我們還發現了另一種的互補函數,它們是在費雪-博美斯特函數的-a和-b這兩項的前面分別乘上滿足特定條件的連續函數。在第四節中,我們討論這三種互補函數的一般形式,並給一些例子和函數的圖形。一些相關的應用和數值的實驗可以當作是後續研究的主題。
In this thesis, we observed that some of the NCP functions were constructed by invertible functions. For example, the famous Fischer-Burmeister function was constructed under this presence. According to the similar structure of the Fischer-Burmeister function, we discovered the other two NCP functions accociated with the invertible functions which were e^t and ln⁡t. We also discovered another type of NCP function which was modified by multiplying the continuous function satisfying the required assumptions infront of the terms -a and -b of the Fischer-Burmeister function . In the section 4, we discussed the general format of the three newly discovered NCP functions and gave some examples and graphs of the different types of NCP functions. We leave some other possible applications and numerical tests of those NCP functions as our future reseach topics.
1 Introduction 1
2 Preliminaries 4
3 Three specific NCP functions and their subdifferential 5
4 Constructions of NCP functions by invertible functions 12
5 Conclusion 26
6 References 26
1. J.H. Alcantara and J.-S. Chen, A novel generalization of the natural residual function and a neural network approach for the NCP, Neurocomputing, vol. 413, pp. 368-382, 2020.

2. J.H. Alcantara, C.-H. Lee, C.T. Nguyen, Y.-L. Chang, and J.-S. Chen, On construction of new NCP functions, Operations Research Letters, vol.48, pp.115-121, 2020.

3. J.-S. Chen, On some NCP-functions based on the generalized Fischer-Burmeister function, Asia-Pacific Journal of Operational Research, vol. 24, pp. 401-420, 2007.

4. J.-S. Chen, C.-H. Ko, and X.-R. Wu, What is the generalization of natural residual function for NCP, Pacific Journal of Optimization, vol. 12, pp. 19-27, 2016.

5. F.H. Clarke, Optimization and Nonsmooth Analysis, Wiley, New York, 1983.

6. F. Facchinei and J.-S. Pang, Finite-dimensional variational inequality and complementarity problems, Springer-Verlag (New York), vol. 1, pp. 1-10, 2003.

7. M. C. Ferris and J.-S. Pang, Engineering and economic applications of complementarity problems, SIAM Review, vol. 39, pp. 669-713, 1997.

8. A. Fischer, A special Newton-type optimization methods, Optimization, vol.24, pp. 269-284, 1992.

9. A. Galantai, Properties and construction of NCP functions, Computational Optimization and Applications, vol. 52, pp. 805-824, 2012.

10. C. Kanzow, Nonlinear complementarity as unconstrained optimization, Journal of Optimization Theory and Applications, vol. 88, pp 139-155, 1996.

11. C. Kanzow, N. Yamashita, and M. Fukushima, New NCP-Functions and Their Properties, Journal of Optimization Theory and Applications, vol. 94, pp 115-135, 1997.

12. C.-H. Lee, C.-C. Hu, and J.-S. Chen, Using invertible functions to construct NCP functions, Linear and Nonlinear Analysis, vol. 6, pp347-369, 2020.

13. T.D. Luca, F. Facchinei, and C. Kanzow, Semismooth Equation Approach To The Solution Of Nonlinear Complementarity Problems, Mathematical Programming, vol. 75, pp. 407–439, 1996.

14. Z.-Q. Luo and P. Tseng, A new class of merit functions for the nonlinear complementarity problem, In: Ferris, M.C., Pang, J.S. (eds.) Complementarity and
Variational Problems: State of the Art, pp. 204-225. SIAM, Philadelphia, 1997.

15. P.-F. Ma, J.-S. Chen, C.-H. Huang, and C.-H. Ko, Discovery of new complementarity functions for NCP and SOCCP, Computational and Applied Mathematics, vol. 37, pp. 5727-5749, 2018.

16. O.L. Mangasarian, Equivalence of the Complementarity Problem to a System of Nonlinear Equations, SIAM Journal on Applied Mathematics, vol. 31, pp. 89–92, 1976.

17. H.-Y. Tsai and J.-S. Chen, Geometric views of the generalized Fischer-Burmeister function and its induced merit function, Applied Mathematics and Computation, vol. 237, pp 31-59, 2014.
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