簡易檢索 / 詳目顯示

回結果列表
研究生： 徐明利
Hsu, Ming-Li
論文名稱： 關於二級錐函數上的一些結果
Some Results on Functions Associated With Second-Order Cone
指導教授： 蔡蓉青
Tsai, Rung-Ching
學位類別： 碩士
Master
系所名稱： 數學系
Department of Mathematics
論文出版年： 2007
畢業學年度： 95
語文別： 中文
論文頁數： 38
中文關鍵詞： 二級錐 、二級錐函數 、二級錐凸函數 、二級錐單調函數
英文關鍵詞： Second-order cone, SOC function, SOC-convex function, SOC-monotone function
論文種類： 學術論文
相關次數： 點閱：215  下載：19 
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

    • 關於二級錐向量值函數在解決二級錐問題及二級錐互補問題上有許多的研究 . 這篇論文是研究二級錐函數及其凹口的性質 , 特別是我們導出二級錐上行列式的一個特性 . 最後 , 我們以另一個方法討論二級錐對數函數單調的性質 .

    The vector-valued functions associated with second-order cones have been much studied in solutions methods for second-order-cone programs (SOCPs) and second-order-cone complementarity programs (SOCCPs). In this paper, we study the SOC-convexity for some function , in particular, we derive some characterization of determinant defined on second-order cones (SOCs). Finally, we discuss the SOC-monotonicity for the lagarithmic function which is approached by different analysis .

    Contents 1. Introduction ….…………………………………………………… 2 2 Preliminary…………………………………………………………..4 3 Main Results on SOC-convex function ………………………8 4 Ongoing work………………………………………………………..30 Reference ............................................37

    [1] J. S. Aujla and H. L. Vasudeva, Convex and monotone operator functions, Annales Polonici Mathematici, vol. 62, pp. 1-11, 1995.

    [2] R. Bhatia, Matrix Analysis, Springer-Verlag, New York, 1997.

    [3] R. Bhatia and K. P. Parthasarathy, Positive definite functions and operator inequalities, Bulletin of London Mathematics Society, vol. 32, pp. 214-228, 2000.

    [4] J.-S. Chen, The convex and monotone functions associated with second-order cone, Optimization, vol. 55, pp. 363-385, 2006.

    [5] J.-S. Chen, X. Chen, and P. Tseng, Analysis of nonsmooth vector-valued functions associated with second-order cones, Mathematical Programming, vol. 101, pp. 95-117,2004.

    [6] U. Faraut and A. Kor'anyi, Analysis on Symmetric Cones, Oxford Mathematical Monographs, Oxford University Press, New York, 1994.

    [7] 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.

    [8] R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press, Cambridge, 1985.

    [9] R. A. Horn and C. R. Johnson, Topics in Matrix Analysis, Cambridge University Press, Cambridge, 1985.

    [10] A. Kor'anyi, Monotone functions on formally real Jordan algebras, Mathematische Annalen, vol. 269, pp. 73-76, 1984.

    [11] K. Löwner, über monotone matrixfunktionen, Mathematische Zeitschrift, vol. 38, pp. 177-216, 1934.

    [12] D. Sun and J. Sun, Semismooth matrix valued functions, Mathematics of Operations Research, vol. 27, pp. 150-169, 2002.

    [13] P. Tseng, Merit function for semidefinite complementarity problems,
    Mathematical Programming, vol. 83, pp. 159-185, 1998.

    QR CODE