研究生: |
李順瑋 Lee, Shun-Wei |
---|---|
論文名稱: |
On the plane curves based on surfaces of NCP functions On the plane curves based on surfaces of NCP functions |
指導教授: |
陳界山
Chen, Jein-Shan |
口試委員: |
陳界山
Chen, Jein-Shan 張毓麟 Chang, Yu-Lin 杜威仕 Du, Wei-Shih |
口試日期: | 2022/06/16 |
學位類別: |
碩士 Master |
系所名稱: |
數學系 Department of Mathematics |
論文出版年: | 2022 |
畢業學年度: | 110 |
語文別: | 中文 |
論文頁數: | 41 |
英文關鍵詞: | NCP functions, curves, convexity and differentiability, global minimum and maximum |
研究方法: | 實驗設計法 、 準實驗設計法 、 參與觀察法 、 紮根理論法 、 主題分析 、 比較研究 、 觀察研究 、 現象分析 |
DOI URL: | http://doi.org/10.6345/NTNU202200824 |
論文種類: | 學術論文 |
相關次數: | 點閱:155 下載:21 |
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In this thesis, we investigate the curves which are intersected by a vertical plane
and surface based on a certain NCP function. We also study convexity and differentiability of the curves which will help us look into the curves efficiently. In most cases, the inflection points of the curves cannot be figured out exactly. Therefore, we turn to estimate the interval where the curves are convex under this situation. With the help of differentiability and convexity, we look for the local minimum or maximum values of the curves accordingly.
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, no. 2, pp. 115-121, 2020.
3. Y.-L. Chang, J.-S. Chen, and C.-Y. Yang, Symmetrization of generalized natu- ral residual function for NCP, Operations Research Letters, vol. 43, no. 4, pp. 354-358, 2015.
4. J.-S. Chen, On some NCP-functions based on the generalized Fischer-Burmeister function, Asia-Pacific Journal of Operational Research, vol. 24, no. 3, pp. 401-420, 2007.
5. 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.
6. J.-S. Chen, J.-F. Li, and J. Wu, A continuation approach for solving binary quadratic program based on a class of NCP-functions, Applied Mathematics and Com- putation, vol. 219, no. 8, pp. 3975-3992, 2012.
7. A. Galantai, Properties and construction of NCP functions, Computational Opti-
mization and Applications, vol. 52, pp. 805–824, 2012.
8. Hoang Tuy, Convex Analysis and global Optimization, second edition, Springer,
Hanoi, Vietnam, 2016.
9. C.-H. Huang, K. -J. Weng, J. -S. Chen, H. -W. Chu, and M. -Y. Li, On four discrete-type families of NCP-functions, Journal of Nonlinear and Convex Analysis, vol. 20, no. 2, pp. 283-306, 2019.
10. C.-H. Lee, C.-C. Hu, and J.-S. Chen, Using invertible functions to construct
NCP functions, Linear and Nonlinear Analysis, vol. 6, no. 3, pp. 347-369, 2020.
11. P.-F. Ma, J.-S. Chen, C.-H. Huang, and C.-H. Ko, Discovery of new comple- mentarity functions for NCP and SOCCP, Computational and Applied Mathematics, vol. 37, no. 5, pp. 5727-5749, 2018.
12. H.-Y. Tsai and J.-S. Chen, Geometric views of the generalized Fischer- Burmeister function and its induced merit function, Applied Mathematics and Com- putation, vol. 237, June 15, pp. 31-59, 2014.