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博碩士論文 etd-0619108-205854 詳細資訊
Title page for etd-0619108-205854
論文名稱
Title
擬單調多值函數之廣義變分不等式的近似鄰近演算法
Approximate Proximal Algorithms for Generalized Variational Inequalities with Pseudomonotone Multifunctions
系所名稱
Department
畢業學年期
Year, semester
語文別
Language
學位類別
Degree
頁數
Number of pages
28
研究生
Author
指導教授
Advisor
召集委員
Convenor
口試委員
Advisory Committee
口試日期
Date of Exam
2008-05-30
繳交日期
Date of Submission
2008-06-19
關鍵字
Keywords
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
Strong convergence, Hilbert space, Pseudomonotone multifunctions, Generalized variational inequalities, Approximate proximal algorithms
統計
Statistics
本論文已被瀏覽 5786 次,被下載 1400
The thesis/dissertation has been browsed 5786 times, has been downloaded 1400 times.
中文摘要
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。
Abstract
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.
目次 Table of Contents
Introduction and Preliminaries 4
Strong Convergence of Approximate Proximal Algorithm 9
Strong Convergence of Bregman-Function-Based Approximate Proximal Algorithm 16
References 25
參考文獻 References
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[5] G. Stampacchia, Variational inequalities, theory and applications of monotone operators, edited by A. Ghizzetti, Edizioni Oderisi, Gubbio, Italy, pp. 101-192, 1969.
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[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.
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