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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 |
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系所名稱 Department |
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畢業學年期 Year, semester |
語文別 Language |
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學位類別 Degree |
頁數 Number of pages |
28 |
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研究生 Author |
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指導教授 Advisor |
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召集委員 Convenor |
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口試委員 Advisory Committee |
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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 |
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統計 Statistics |
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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 |
[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. |
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