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Let be a real Hilbert space. Let , be bounded monotone mappings with , where and are closed convex subsets of satisfying certain conditions. Suppose the equation has a solution in . Then explicit iterative methods are constructed that converge strongly to such a solution. No invertibility assumption is imposed on , and the operators and need not be defined on compact subsets of .
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Pseudo-monotone complementarity problems in Hilbert space 总被引:1,自引:0,他引:1
In this paper, some existence results for a nonlinear complementarity problem involving a pseudo-monotone mapping over an arbitrary closed convex cone in a real Hilbert space are established. In particular, some known existence results for a nonlinear complementarity problem in a finite-dimensional Hilbert space are generalized to an infinite-dimensional real Hilbert space. Applications to a class of nonlinear complementarity problems and the study of the post-critical equilibrium state of a thin elastic plate subjected to unilateral conditions are given.This research was partially supported by the National Science Foundation Grant DMS-89-13089, Department of Energy Grant DE-FG03-87-ER-25028, and Office of Naval Research Grant N00014-89-J-1659. The authors would like to express their sincere thanks to Professor S. Schaible, School of Administration, University of California, Riverside, for his helpful suggestions and comments. They also thank the referees for their comments and suggestions that improved this paper substantially. 相似文献
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介绍了用三步迭代算法求解A-极大单调算子的不动点问题和用预解算子研究包含问题的解.同时给出了在某些条件下,三步迭代算法的收敛性.该文中的结论是在Noor,Huang的算法及Ram U.Verma的背景下启发得到. 相似文献
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Weak Convergence Theorem by an Extragradient Method for Nonexpansive Mappings and Monotone Mappings 总被引:9,自引:0,他引:9
In this paper, we introduce an iterative process for finding the common element of the set of fixed points of a nonexpansive
mapping and the set of solutions of the variational inequality problem for a monotone, Lipschitz-continuous mapping. The iterative
process is based on the so-called extragradient method. We obtain a weak convergence theorem for two sequences generated by
this process 相似文献
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雷飞燕 《纯粹数学与应用数学》2010,26(3):417-419,425
建立伪单调非线性互补问题在实Hilbert空间任意闭凸锥上的解的存在性理论,特别把互补问题在有限维实Hilbert空间上的一些重要理论推广到无限维实Hilbert空间,还证明了解的存在的可行性理论. 相似文献
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In this paper, we introduce and study a new class of general strongly nonlinear quasivariational inequalities and construct a general iterative algorithm by using the projection method. We establish the existence of a unique solution for general strongly nonlinear quasivariational inequalities involving relaxed Lipschitz, relaxed monotone, and strongly monotone mappings; we obtain the convergence and stability of the iterative sequences generated by the algorithm. Our results extend, improve, and unify many known results due to Bose, Noor, Siddiqi-Ansari, Verma, Yao, Zeng, and others. 相似文献
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In this article,we introduce a hybrid iterative scheme for finding a common element of the set of solutions for a generalized equilibrium problems,the set of common fixed point for a family of infinite... 相似文献
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首先给出了Hilbert空间中Lipschitz单调映像变分不等式解的迭代格式,并证明了其收敛性.作为应用,证明了Hilbert空间中Lipschitz伪压缩映像的强收敛定理,扩展了已知的相关结果. 相似文献
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The mean transformations M(A,?B) are linear mappings and they are analogues of the matrix means of A,?B?≥?0. They are defined by operator monotone functions. In this article several properties are described and a part of them characterize the concept. 相似文献
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T. Pennanen R. T. Rockafellar M. Thé ra 《Proceedings of the American Mathematical Society》2002,130(8):2261-2269
This paper gives sufficient conditions for graphical convergence of sums of maximal monotone mappings. The main result concerns finite-dimensional spaces and it generalizes known convergence results for sums. The proof is based on a duality argument and a new boundedness result for sequences of monotone mappings which is of interest on its own. An application to the epi-convergence theory of convex functions is given. Counterexamples are used to show that the results cannot be directly extended to infinite dimensions.
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S.Z. Németh 《Journal of Mathematical Analysis and Applications》2009,350(1):340-893
In this paper we present a recursion related to a nonlinear complementarity problem defined by a closed convex cone in a Hilbert space and a continuous mapping defined on the cone. If the recursion is convergent, then its limit is a solution of the nonlinear complementarity problem. In the case of isotone projection cones sufficient conditions are given for the mapping so that the recursion to be convergent. 相似文献
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Habtu Zegeye 《Journal of Mathematical Analysis and Applications》2008,343(2):663-671
Let E be a uniformly convex and 2-uniformly smooth real Banach space with dual E∗. Let be a Lipschitz continuous monotone mapping with A−1(0)≠∅. For given u,x1∈E, let {xn} be generated by the algorithm xn+1:=βnu+(1−βn)(xn−αnAJxn), n?1, where J is the normalized duality mapping from E into E∗ and {λn} and {θn} are real sequences in (0,1) satisfying certain conditions. Then it is proved that, under some mild conditions, {xn} converges strongly to x∗∈E where Jx∗∈A−1(0). Finally, we apply our convergence theorems to the convex minimization problems. 相似文献
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《Optimization》2012,61(6):765-778
Isac and Németh [G. Isac and A. B. Németh, Projection methods, isotone projection cones and the complementarity problem, J. Math. Anal. Appl. 153 (1990), pp. 258–275] proved that solving a coincidence point equation (fixed point problem) in turn solves the corresponding implicit complementarity problem (nonlinear complementarity problem) and they exploited the isotonicity of the metric projection onto isotone projection cones to solve implicit complementarity problems (nonlinear complementarity problems) defined by these cones. In this article an iterative algorithm is studied in connection with an implicit complementarity problem. It is proved that if the sequence generated through the defined algorithm is convergent, then its limit is a solution of the coincidence point equation and thus solves the implicit complementarity problem. Sufficient conditions are given for this sequence to be convergent for implicit complementarity problems defined by isotone projection cones, extending the results of Németh [S.Z. Németh, Iterative methods for nonlinear complementarity problems on isotone projection cones, J. Math. Anal. Appl. 350 (2009), pp. 340–370]. Some existing concepts from the latter paper are extended to solve the problem of finding nonzero solutions of the implicit complementarity problem. 相似文献
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在q-一致光滑和严格凸的Banach空间中,研究了无穷个严格伪压缩映射的混合迭代算法,证明了由这种新的算法产生的序列强收敛于这无穷个严格伪压缩映射的公共不动点,并且是变分不等式〈(I-A)x,J_q(p-x)〉≤0,p∈(n i=l)F(T_i)的解.论文推广和改进了一些前人的相应结论. 相似文献