跳到主要內容

臺灣博碩士論文加值系統

(18.97.14.81) 您好!臺灣時間:2024/12/15 05:00
字體大小: 字級放大   字級縮小   預設字形  
回查詢結果 :::

詳目顯示

: 
twitterline
研究生:蕭丞志
研究生(外文):Cheng-chih Hsiao
論文名稱:擬單調多值函數之廣義變分不等式的近似鄰近演算法
論文名稱(外文):Approximate Proximal Algorithms for Generalized Variational Inequalities with Pseudomonotone Multifunctions
指導教授:姚任之
指導教授(外文):Jen-chih Yao
學位類別:碩士
校院名稱:國立中山大學
系所名稱:應用數學系研究所
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:2008
畢業學年度:96
語文別:英文
論文頁數:28
中文關鍵詞:廣義變分不等式擬單調多值函數希爾伯特空間強收斂性近似鄰近演算法
外文關鍵詞:Strong convergenceHilbert spacePseudomonotone multifunctionsGeneralized variational inequalitiesApproximate proximal algorithms
相關次數:
  • 被引用被引用:0
  • 點閱點閱:165
  • 評分評分:
  • 下載下載:8
  • 收藏至我的研究室書目清單書目收藏:0
在文章裡面,我們建立一些在兩種演算法下的強收斂結果,來解決擬單調多值函數的廣義變分不等式問題。其一為一般進似鄰近演算法,另一為一般布瑞格曼函數近似鄰近演算法。
In this paper, we establish several strong convergence results of general approximate proximal algorithm and general Bregman-function-based approximate proximal algorithm for solving the generalized variational inequality problem with pseudomonotone multifunction.
Introduction and Preliminaries 4
Strong Convergence of Approximate Proximal Algorithm 9
Strong Convergence of Bregman-Function-Based Approximate Proximal Algorithm 16
References 25
[1] R.E. Bruck, An iterative solution of a variational inequality for certain monotone operator in a Hilbert space, Bulletin of the American Mathematical Society, Vol. 81, pp. 890-892, 1975. Corrigendum in Vol. 82, p. 353, 1976.
[2] J.C. Yao, Multi-valued variational inequalities with K-pseudomonotone operators, Journal of Optimization Theory and Applications, Vol. 83, pp. 391-403, 1994.
[3] J.S. Guo, J.C. Yao, Variational inequalities with nonmonotone operators, Journal of Optimization Theory and Applications, Vol. 80, pp. 63-74, 1994.
[4] J.C. Yao, J.S. Guo, Variational and generalized variational inequalities with discontinuous mappings, Journal of Mathematical Analysis and Applications, Vol. 182, pp. 371-392, 1994.
[5] G. Stampacchia, Variational inequalities, theory and applications of monotone operators, edited by A. Ghizzetti, Edizioni Oderisi, Gubbio, Italy, pp. 101-192, 1969.
[6] G.J. Hartman, G. Stampacchia, On some nonlinear elliptic differential functional equations, Acta Mathematica, Vol. 115, pp. 271-310, 1966.
[7] J.C. Yao, Variational inequality, Applied Mathematics Letters, Vol. 5, pp. 39-42, 1992.
[8] J.C. Yao, Variational inequalities with generalized monotone operators, Mathematics of Operations Research, Vol. 19, pp. 691-705, 1994.
[9] R.S. Burachik, J.O. Lopes, B.F. Svaiter, An outer approximation method for the variational inequality problem, SIAM Journal on Control and Optimization, Vol. 43, pp. 2071-2088, 2005.
[10] A.N. Iusem, On some properties of paramonotone operators, Journal of Convex Analysis, Vol. 5, pp. 269-278, 1998.
[11] F.E. Browder, Nonlinear operators and nonlinear equations of evolution in Banach spaces, in Nonlinear Functional Analysis, AMS, Providence, RI, pp. 1-308, 1976.
[12] M.V. Solodov, B.F. Svaiter, An inexact hybrid generalized proximal point algorithm and some new results on the theory of Bregman functions, Mathematics of Operations Research, Vol. 25, pp. 214-230, 2000.
[13] S.C. Fang, E.L. Peterson, Generalized variational inequalities, Journal of Optimization Theory and Applications, Vol. 38, pp. 363-383, 1982.
[14] L.C. Ceng, J.C. Yao, Approximate proximal algorithms for generalized variational inequalities
with pseudomonotone multifunctions, Journal of Computational and Applied Mathematics, Vol. 213(2), pp. 423-438, 2008.
[15] CHEN, G., and TEBOULLE, M., Convergence Analysis of A Proximal-like Minimization Algorithm Using Bregman Functions, SIAM Journal on Optimization, Vol. 3, pp. 538-543, 1993.
QRCODE
 
 
 
 
 
                                                                                                                                                                                                                                                                                                                                                                                                               
第一頁 上一頁 下一頁 最後一頁 top