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| 研究生： |
洪浩峰 Hao-Feng Hung |
|---|---|
| 論文名稱： |
一些跟circular cone有關的不等式 Some inequalities associated with circular cone |
| 指導教授： |
陳界山
Chen, Jein-Shan |
| 學位類別： |
碩士 Master |
| 系所名稱： |
數學系 Department of Mathematics |
| 論文出版年： | 2013 |
| 畢業學年度： | 101 |
| 語文別： | 中文 |
| 論文頁數： | 8 |
| 中文關鍵詞： | Second-order cone 、circular cone 、spectral factorization 、determinant 、trace |
| 論文種類： | 學術論文 |
| 相關次數： | 點閱：192 下載：9 |
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The circular cone is a pointed closed convex cone having hyperspherical sections orthogonal to its axis of revolution about which the cone is invariant to rotation.
In this section, we establish some inequalities associated with circular cone, which we believe that they will be useful for further analyzing properties of $f^{\mathcal{L}_\theta}$ and proving the convergence of interior point methods for optimization problems involved in circular cones.
[1] J. Dattorro, Convex Optimization and Euclidean Distance Geometry, Meboo Publishing,California, 2005.
[2] J-C Zhou and J-S Chen, Properties of circular cone and spectral factorization associated with circular cone, to appear in Journal of Nonlinear and Convex Analysis, 2013.
[3] Y-L Chang, C-Y Yang, and J-S Chen, Smooth and nonsmooth analyses of vectorvalued functions associated with circular cones, Nonlinear Analysis: Theory, Methods and Applications, vol. 85, pp. 160-173, July, 2013.
[4] 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.
[5] M-L Hsu and R-C Tsai, Some Results on Functions Associated With Second-Order Cone, June, 2007.
[6] J-S Chen, The convex and monotone functions associated with second-order cone, Optimization, vol. 55, no. 4, pp. 363-385, 2006.
[7] J-S Chen, X. Chen, and P. Tseng, Analysis of nonsmooth vector-valued functions associated with second-order cone, Mathematical Programming, vol. 101, no. 1, pp.95-117, 2004.
