簡易檢索 / 詳目顯示
| 研究生： |
莊國裕 Chuang, Kuo-Yu |
|---|---|
| 論文名稱： |
二階錐跡函數的自協調性 The self-concordancy of the trace functions on SOCs |
| 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： | 2015 |
| 畢業學年度： | 103 |
| 語文別： | 英文 |
| 論文頁數： | 18 |
| 中文關鍵詞： | 二階錐 、跡函數 、自協調性 |
| 英文關鍵詞： | Second-order cone, Trace function, Self-concordant |
| 論文種類： | 學術論文 |
| 相關次數： | 點閱：160 下載：23 |
| 分享至: |
| 查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報 |
自協調性函數在內點法的使用上扮演了重要的角色。在這篇論文中我們檢驗了一些原始函數和其二階錐跡函數的自協調性及強自協調性，我們想要去建立原始函數和其二階錐跡函數的強自協調性的對應關係。
The strongly non-degenerate self-corcordant functions are the key to applying interior-point method. In this paper, we check the self-concordancy and the strongly non-degenerate self-concordancy for some examples, and we want to establish strongly non-degenerate self-concordancy of some functions associated with second-order cone, called SOC trace functions.
[1] Y.-L. Chang and J.-S. Chen Convexity of symmetric cone trace functions in Euclidean Jordan Algebra, Journal of Nonlinear and Convex Analysis , vol. 14, no.1, pp. 53-61, 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] J. Renegar A Mathematical View of Interior-Point Methods in Convex Optimization, MPS-SIAM Series on Optimization, Philadelphia, PA, USA, 2001.
[4] M. Fukushima, Z.-Q. Luo and P. Tseng, Smoothing functions for second-order cone complementarity problems, SIAM Journal on Optimization, vol. 12, pp. 436-460, 2002.
[5] J. Faraut and A. Koranyi, Analysis on symmetric Cones, Oxford Mathematical Monographs, Oxford University Press, New York, 1994.
[6] F. Kruse and M. Ulbrich, A self-concordant interior point approach for optimal control with state constraints, SIAM Journal on Optimization, vol. 25, pp. 770-806, 2015.
[7] A. Auslender, Penalty and barrier methods: a unified framework, SIAM Journal on Optimization, vol. 10, pp. 211-230, 1999.
[8] A. Auslender, Variational inequalities over the cone of semide nite positive symmetric matrices and over the Lorentz cone, Optimization Methods and Software, vol. 18, pp. 359-376, 2003.
[9] A. Auslender and H. Ramirez, Penalty and barrier methods for convex semidefinite programming, Mathematical Methods of Operations Research, vol. 63, pp. 195-219, 2006.
[10] H. Bauschke, O. Guler, A. S. Lewis and S. Sendow, Hyperbolic polynomial and convex analysis, Canadian Journal of Mathematics, vol. 53, pp. 470-488, 2001.
[11] A. Ben-Tal and A. Nemirovski, Lectures on Modern Convex Optimization: Analysis, Algorithms and Engineering Applications, MPS-SIAM Series on Optimization. SIAM, Philadelphia, USA, 2001.
[12] J.-S. Chen, X. Chen and P. Tseng, Analysis of nonsmooth vector-valued functions associated with second-order cone, Mathmatical Programming, vol. 101, pp. 95-117, 2004.
[13] J.-S. Chen, The convex and monotone functions associated with second-order cone, Optimization, vol. 55, pp. 363-385, 2006.
[14] R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press, Cambridge, 1986.
