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| 研究生： |
黃偉 Huang, Wei |
|---|---|
| 論文名稱： |
一個閉凸集上的凸函數之研究 The Study on Convex Functions in a Closed Convex Set |
| 指導教授： |
張毓麟
Chang, Yu-Lin |
| 學位類別： |
碩士 Master |
| 系所名稱： |
數學系 Department of Mathematics |
| 論文出版年： | 2016 |
| 畢業學年度： | 104 |
| 語文別： | 英文 |
| 論文頁數： | 19 |
| 中文關鍵詞： | 凸 、最佳化 、圓錐 、跡函數 、半正定 |
| 英文關鍵詞： | Convexity, Optimization, Circular Cone, Trace Function, Positive Semi-definiteness |
| DOI URL： | https://doi.org/10.6345/NTNU202204540 |
| 論文種類： | 學術論文 |
| 相關次數： | 點閱：213 下載：31 |
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無中文摘要
We extend to a problem of two-variable function from a monotone condition for the convexity of trace function associated with circular cone in this paper. This structure was based on the Schur Complement Theorem. By smoothing the problem, the greatest benefit is spared the solving time and we believe this establishment will useful in many fields.
[1] Y.-L. Chang, C.-Y. Yang and J.-S. Chen Smooth and nonsmooth analyses of vector-valued functions associated with circular cones, Nonlinear Analysis: Theory, Methods and Applications, vol. 85, pp. 160-173, 2013.
[2] J.-S. Chen, T.-K Liao and S.-H. Pan Using Schur Complement Theorem to prove convexity of some SOC-functions, Journal of Nonlinear and Convex Analysis, vol. 13, no. 3, pp. 421-431, 2012.
[3] Jinchuan Zhou, J.-S. Chen and H.-F. Hung Circular cone convexity and some inequalities associated with circular cones, Journal of Inequalities and Applications, 2013:571, 2013.
[4] Jinchuan Zhou and J.-S. Chen, Properties of circular cone and spectral factorization associated with circular cone, Journal of Nonlinear and Convex Analysis, vol. 14, no. 4, pp. 807-816, 2013.
[5] C.-Y. Yang, Y.-L. Chang and J.-S. Chen, Analysis of nonsmooth vector-valued functions associated with infinite-dimensional second-order cones, Nonlinear Analysis: Theory, Methods and Applications, vol. 74, no. 16, pp. 5766-5783, 2011.
[6] R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press, Cambridge, 1986.
[7] T.-W. Wu and Y.-L. Chang, The convexity of circular cone trace functions, Master’s thesis, National Taiwan Normal University, Taipei, Taiwan, 2015.
