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研究生: 劉彥迪
Yan-Di Liu
論文名稱: 用來解一個系統的等式與不等式的新平滑函數
New smoothing functions for solving a system of equalities and inequalities
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: 2014
畢業學年度: 102
語文別: 中文
論文頁數: 18
中文關鍵詞: 平滑函數系統的等式與不等式收斂
英文關鍵詞: Smoothing function, system of equations and inequalities, convergence
論文種類: 學術論文
相關次數: 點閱:190下載:24
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  • In this paper, we propose a family of new smoothing functions for solving a system of equalities and inequalities. We also investigate a monotone algorithm and show that it is globally and locally superlinearly convergent under suitable assumptions

    1 Introduction 1 2 Smooth reformulation 2 3 A smoothing-type algorithm 7 4 Global convergence 11 5 Local superlinear convergence 15 6 References 17

    [1] R. bhatia, Matrix Analysis, Springer-Verlag, New York, 1997
    [2] J.W. Daniel, Newton’s method for nonlinear inequalities, Numerical Mathematics,vol. 21, pp. 381-387, 1973.
    [3] R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press,Cambridge, 1986.
    [4] Z-H. Huang, Y. Zhang, and W. Wu, A smoothing-type algorithm for solving stsyem of inequalities, Journal of Computational and Applied Mathematics, vol. 220,pp. 355-363, 2008.
    [5] D.Q. Mayne, E. Polak, and A.J. Heunis, Solving nonlinear inequalities in a finite number of iterations, Optimization Theory and Applications, vol. 33, pp. 207-221, 1981.
    [6] M. Sahba, On the solution of nonlinear inequalities in a finite number of iterations,Numerical Mathematics, vol. 46, pp. 229-236, 1985.
    [7] J.M. Schott, Matrix Analysis for Statistics, 2nd edition, John Wiley, New Jersey,2005.
    [8] H-X. Ying, Z-H. Huang, and L. Qi, The convergence of a Levenberg-Marquard
    method for the l2-norm solution of nonlinear inequalities, Numerical Functional Analysis and Optimization, vol. 29, pp. 687-716, 2008.
    [9] Y. Zhang and Z-H. Huang, A nonmonotone smoothing-type algorithm for solving a system of equalities and inequalities, Journal of Computational and Applied
    Mathematics, vol. 233, pp. 2312-2321, 2010.
    [10] J. Zhu and B. Hao, A new non-interior continuation method for solving a system of equalities and inequalities, submitted manuscript, 2014.
    [11] Robert G. Bartle, The Elements of Real Analysis, Second Edition
    [12] S.L. HU , Z-H. Huang and P. Wang , A non-monotone smoothing Newton algorithm for solving nonlinear complementarity problems, Optimization Methods and
    Software , vol. 24, pp. 447-460, 2009

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