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研究生:劉彥迪
研究生(外文):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
論文名稱(外文):New smoothing functions for solving a system of equalities and inequalities
指導教授:陳界山陳界山引用關係
指導教授(外文):Jein-Shan Chen
學位類別:碩士
校院名稱:國立臺灣師範大學
系所名稱:數學系
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
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
外文關鍵詞:Smoothing functionsystem of equations and inequalitiesconvergence
相關次數:
  • 被引用被引用:0
  • 點閱點閱:195
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  • 下載下載:15
  • 收藏至我的研究室書目清單書目收藏:0
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
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[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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