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論文名稱 Title |
變分不等式之研究 Variational Inequalities |
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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 |
37 |
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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 |
2007-06-15 |
繳交日期 Date of Submission |
2007-07-18 |
關鍵字 Keywords |
偽單調算子、變分不等式、多值偽單調映射、廣義單調算子、強制控制 Pseudomonotone, Variational Inequalities, Generalized monotonicity, Cx-pseudomonotone, Corecivity |
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統計 Statistics |
本論文已被瀏覽 5709 次,被下載 25 次 The thesis/dissertation has been browsed 5709 times, has been downloaded 25 times. |
中文摘要 |
在這個論文中,我報告近年來有限維空間中廣義單調算子 上的變分不等式存在結果 |
Abstract |
In this thesis,we report recent results on existence for variational inequalities in infinite-dimensional spaces under generalized monotonicity. |
目次 Table of Contents |
I. Abstract…P2 II. Key Words…P2 III. Introduction…P3-6 IV. Preliminaries…P7-13 V. Existence and Uniqueness Results…P14-18 VI. Application to Optimization Problems…P19-24 VII. Bibliography…P25-34 |
參考文獻 References |
[1] Allen, G., Variational Inequalities, Complementarity Problems, and Duality Theorems. J., Math. Anal. Appl, 58 1-10, 1977. [2] Aubin, J. P., Mathematical Metho ds of Game and Economic Theory, revised ed., Stud.Math. North-Holland, Amsterdam. Appl, 7, North Holland, Amsterdam, 1982. [3] Baiocchi, C., and A., Capelo, Variational and Quasi-Variational Inequalities, John Wiley and Sons, New York, London, 1984. [4] Barbu, V., and Precupanu, Th. Conrexity and Optimization in Banach Spaces. Sijtho. and No ordho., Bucarest, Romania, 1986. [5] Borwein, J. M., and Fitzpatrick, S., Local Boundedness of Monotone Operators under Minimal Hypotheses. Bull. Austral. Math. Soc, 1988. [6] Bourbaki, N., Espaces Vectoriels Topologiques, Hermann, Paris, 1966. [7] Br¡¦ezis, H., Equations etinequations nonlineaires dansles espaces vectoriels endualite, Ann. Inst, Fourier 18, 115-175. 1968. [8] Browder, F. E., Nonlinear elliptic boundary value problems, Bull. Am.Math. Soc. 69, 862-874, 1963. [9] Browder, F. E., On the Unification of the Calculus of Variations and the Theory of Monotone Nonlinear Operators in Banach Spaces. Proc.Nat. Acad. Sci. U.S.A, 56419-425, 1966. [10] Browder, F., Coincidence theorems, minimax theorems, and variational inequalities, Contemporary Math. 26, 67-80, 1984. [11] Chadli, O., Chbani, Z., and H.Riahi, Recession Methods for Equilibrium Problems and Applications to Variational and Hemivariational Inequality, Discrete Contin. Dyn. Syst, 5, 185-195, 1999. [12] Chadli, O., Chbani, Z., and H.Riahi, Equilibrium Problems with Generalized Monotone Bifunctions and Applications to Variational Inequality,J., Optimization Theory Appl, 105, 299-323, 2000. [13] Chan, D., and J. S., Pang, The generalized quasi-variational inequality problem, Math. Oper. Res, 7, 211-222, 1982. [14] Chowdhury, M. and K. K. Tan, Applications of pseudo-monotone operators with some kind of upper semicontinuity in generalized quasivariational inequalities on non-compact sets, Proc. Am. Math. Soc. 10,2957-2968, 1998. [15] Deimling, K., Nonlinear Functional Analysis. Springer-Verlag, Berlin,1985. [16] Ekeland, I., and Temam, R., Convex Analysis and Variational Problems. North-Holland, Amsterdam,1976. [17] Fan, K., A generalization of Tychono. ¡¦s fixed point theorem, Math.Ann, 142, 305-310, 1961. [18] Fang, S. C., and E. L., Peterson, generalization Variational Inequality,J., Optimization Theory Appl, 38, 363-383, 1982. [19] Guo, J. S., and Yao, J. C., variational inequality with nonmonotone operators, J., Optimization Theory Appl, 80(1), 63-74, 1994. [20] Glowinski, R., Lions, J. L., Tremolieres, R., Numerical Analysis of Variational Inequalities, North-Holland, Amsterdam, Holland, 1981. [21] Giannessi, F., Maugeri, A., Variational Inequalities and Network Equilibrium Problems,Plenum Press, New York, 1995. [22] Giannessi, F., Maugeri, A., Pardalos, P. M., Equilibrium Problems :Nonsmo oth Optimization and Variational Inequality Models, Kluwer Academic Press, Dordrecht, Holland, 2001. [23] Giannessi, F., Maugeri, A., Variational Inequalities and Network Equilibrium Problems, Plenum Press, New York, 1995. [24] Glowinski, R., Lions, J. L., R. Tre molie res, Numerical Analysis of Variational Inequalities, North-Holland, Amsterdam,1981. [25] Gwinner, J., On Fixed Points and Variational Inequalities-A Circular Tour. Nonlinear Anal. Theory Meth. Appl, 5 565-583, 1980. [26] Harker, P. T., and Pang, J. S., Finite-dimensional Variational Inequality and Nonlinear Complementarity Problems : A Survey of Theory, Algorithms and Applications. Math. Programming, Series B, 48, 161-220,1990. [27] Hartman, G. J., and Stampacchia, G., On Some Nonlinear Elliptic Differential Functional Equations. Acta. Math, 115, 153-188, 1966. [28] He, B. S., Liao, L. Z., Improvement of some projection methods for monotone nonlinear variational inequalities, J., Optim. Theory Appl,2002. [29] Holmes, R. B., Geometric Functional Analysis and Its Applications.Springer-Verlag, NY, 1975. [30] Isac, G., Complementary Problems, Lecture Notes in Mathhematics,1528, Springer-Verlag, Berlin Heidelberg, 1992. [31] Karamardian, S., Complementary programming, P.h.D. Thesis, University of California, Berkley, 1966. [32] Karamardian, S., The Nonlinear Complementarity Problem with Applications. Parts I and II. J., Optim. Theory Appl, 487-98 and 167-181,1969. [33] Karamardian, S., Complementarity Problems over Cones with Monotone and Pseudomonotone Maps. J., Optim. Theory. Appl, 19 (2),227-232, 1976. [34] Karamardian, S., and Schaible, S., Seven Kinds of Monotone Maps. J.,Optim. Theory Appl, 66, 1990, 37-46, 1990. [35] Kinderlehrer, D., and Stampacchia, G., An Introduction to Variational Inequalities and Their Applications. Academic Press, NY, 1980. [36] Knaster, B., Kuratowski, G., and S. Mazukiewicz, Ein bewies des fixpunktsatzes fur n-dimensional simplexe, Fund. Math, 14, 132-137, 1929. [37] Lions, J. L., and Stampacchia, G., Variational Inequalities. Comm. Pure Appl. Math, 20, 1967, 493-519, 1967. [38] Luna, G., A Remark on the Nonlinear Complementarity Problem. Proc.Amer. Math. Soc, 48, 1975, 132-134, 1975. [39] Minty, G. J., Monotone (Nonlinear) Operators in Hilbert Space. Duke Math, J. 29, 341-346, 1962. [40] Minty, G., Monotonicity method for the solution of nonlinear equations in Banach spaces, Proc. Natl. Acad. Sci. USA, 50, 1038-1041, 1963. [41] Mancino, O., and G. Stampacchia, Convex programming and variational inequalities, J., Optimization Theory Appl, 1972. Problems. SIAM Rev,1974. [42] More, J. J., and W. C., Rheinboldt, On P- and S-functions and related classes of n-dimensional nonlinear mappings, Linear Algebra Appl, 6,45-68, 1973. [43] Mosco, U., A Remark on a Theorem of F. E., Browder. J. Math. Anal. Appl, 20, 90-93, 1967. [44] Mosco, U., On Stationary Points and the Complementarity Problem. J.,Math. Anal. Appl, 21, 351-356, 1979. [45] Noor, M.A. General variational inequalities, Appl. Math. Lett, 130, 344-353, 1988. [46] Noor, M. A., Inayat Noor, K., Rassias, T h. M. Some aspects of variational inequalities, J., Comput. Appl. Math, 1993. [47] Noor, M. A., Th. M. Rassias, A class of pro jection methods for general variational inequalities, J., Math. Anal. Appl, 2002. [48] Noor, M. A., Proximal point algorithms for variational inequalities,Nonlinear Funct. Anal. Appl, 2002. [49] Noor, M. A. Wang, Y., Xiu, N., Some new pro jection metho ds for variational inequalities, Appl. Math. Comput, 2003. [50] Oden, J. T., Kikuchi, N., Theory of variational inequalities with applications to problems of owthrough porous media, Int. J., Engng. Sci,1980. [51] Parida, J. and A. Sen, A variational-like inequality for multifuctions with applications, J. Math. Anal. Appl. 924, 73-81, 1987. [52] Patriksson, M., Nonlinear Programming and Variational Inequalities :A Unified Approach, Kluwer Academic Publishers, Dordrecht, Holland,1998. [53] Phelps, R R, Convex Functions, Monotone Operators and Di.erentiability. Lecture Notes in Mathematics, 1364, Springer-Verlag, 1993. [54] Rockafellar, R. T., Monotone operators and the proximal point metho d,SIAM J. Control. Optim, 1976. [55] Saigal, R., Extension of the generalized complementarrity problem,Math. Oper. Res, 1, 260-266, 1976. [56] Schmitt, K. and Le, V. K., Global Bifurcation in Variational Inequalities.Application to Obstacle and Unilateral Problems, Springer, New York,1997. [57] Schuricht, F., Bifurcation from minimax solutions by variational inequalities, Math. Nachr. MathSciNet, 1991. [58] Shih, M. H., and K. K., Tan, Brower-Hartmann-Stampacchia variational inequalities for mulit-value monotone operators, J., Math. Anal, 1988. [59] Solodov, M. V., Tseng, P., Modified pro jection type methods for monotone variational inequalities, SIAM J. Control Optim, 1996. [60] Stampacchia, G., Formes bilineaires coercivites surles ensembles convexes, C. R., Acad. Sci. Paris, 1968. [61] Stampacchia, G., Variational inequalities, in Theory and Applications of Monotone Operators, A. Ghizzetti ed., Proceedings of the NATO Advanced Study Institute, Venice Italy (Edizioni Oderisi, Gubbio, Italy),102-192, 1969. [62] Yao, J. C., Variational Inequalities with generalized monotone operators,Math. Oper. Res, 19 (3), 691-705, 1994. [63] Yao, J. C., Existence of generalized variational inequalities, Oper. Res Lett, 15, 35-40, 1994. [64] Yu, S. J., and Yao, J.C., On Variational Inequalities, Journal of Optimization Theory and Applications, 2001. [65] Zhu, D. L., Marcotte, P., An extended descent frame work forvariational inequalities, J., Optim. Theory Appl, 1994. |
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