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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:129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. Introduction 1 2. Preliminaries 5 3. The differentiability of the curves 7 4. The convexity of the curves 13 5. The local minimum and maximum of the curves 31 6. Summary 40 References 40

    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.

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