共查询到16条相似文献,搜索用时 69 毫秒
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通过构造的一类严格分离当前点与解集的超平面得到了一类解伪单调变分不等式的修正二次投影算法,该算法对He Yiran的算法进行了修正.从而建立了解伪单调变分不等式二次投影算法的一种框架结构.证明了该算法生成的无穷序列具有的全局收敛性,在具备某种局部误差界和Lipchitz连续条件下给出了收敛率分析.并给出了该算法的数值演算结果. 相似文献
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考虑了经典变分不等式问题的外梯度投影算法.基于Fan和Qin提出的带惯性项的外梯度投影算法,在映射是伪单调和一致连续的假设下,证明了算法弱收敛到变分不等式问题的解.同时,数值实验验证了算法的适用性.所得结果改进和推广了最新文献中主要结果. 相似文献
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本文在实Hilbert空间上引入了一类求解集值混合变分不等式新的自适应惯性投影次梯度算法.在集值映射T为f-强伪单调或单调的条件下,我们证明了由该自适应惯性投影次梯度算法所产生的序列强收敛于集值混合变分不等式问题的的唯一解. 相似文献
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本文在Hilbert空间上引入了一个新迭代算法,找到了伪单调变分不等式问题的解集与伪非扩张映射的不动点集的公共元.通过修改的超梯度算法,得到了弱收敛定理.所得结果推广和提高了许多最新结果. 相似文献
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荣祯 《应用泛函分析学报》2012,14(1):109-112
给出了求解单调变分不等式的两类迭代算法.通过解强单调变分不等式子问题,产生两个迭代点列,都弱收敛到变分不等式的解.最后,给出了这两类新算法的收敛性分析. 相似文献
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1.引 言 设C Rn为非空闭凸集,为连续映射.变分不等式问题,记为VI(F,C),是求满足上述条件的向量x∈C变分不等式问题在工程力学,交通运输,经济运筹等方面具有广泛的应用并越来越受到人们的重视 [2,3] 求解变分不等式问题有很多解法,其中最简单的是投影 相似文献
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代宏霞 《应用泛函分析学报》2008,10(1):39-43
在算子的分裂技巧基础上介绍了求解伪单调广义混合变分不等式的改进五步预解算法,算法的收敛性只要求算子的g-伪单调和g—Lipschitz连续性,算子的伪单调比单调更弱.本文的新算法推广了文献中某些已有的结果. 相似文献
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本文通过对「1」中相应结构的讨论与改进,利用变分不等式求解技巧,讨论了Hilbert空间中一类广义变分不等式的解的迭代算法及其收敛性,指出了文「1」中主要结果的证明的一些不足之处,本文所得结果推广并改进了「1」的相应结论。 相似文献
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万升联 《数学物理学报(A辑)》2021,(1):237-244
该文研究一种新的解变分不等式的二次投影算法.通过构造一类新的严格分离当前迭代和变分不等式解集的超平面,进而建立了解决伪单调变分不等式投影算法的一种新的框架.通过改进已有结果的证明方法,证明了该算法生成的无穷序列是全局收敛的,并且在局部误差和Lipschitz条件下给出了收敛率分析. 相似文献
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In this paper, we prove that each monotone variational inequality is equivalent to a two-mapping variational inequality problem. On the basis of this fact, a new class of iterative methods for the solution of nonlinear monotone variational inequality problems is presented. The global convergence of the proposed methods is established under the monotonicity assumption. The conditions concerning the implementability of the algorithms are also discussed. The proposed methods have a close relationship to the Douglas–Rachford operator splitting method for monotone variational inequalities. 相似文献
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In this paper, we introduce and study a new class of variational inequalities, which is called the generalized mixed variational inequality. Using essentially the resolvent operator concept, we establish the equivalence between the generalized mixed variational inequalities and the system of resolvent equations. This equivalence is used to suggest a number of new iterative algorithms for solving the variational inequalities. Several special cases are discussed which can be obtained from the main results of this paper. 相似文献
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Q. H. Ansari Z. Khan A. H. Siddiqi 《Journal of Optimization Theory and Applications》2005,127(2):263-283
In this paper, we introduce weighted variational inequalities over product of sets and system of weighted variational inequalities.
It is noted that the weighted variational inequality problem over product of sets and the problem of system of weighted variational
inequalities are equivalent. We give a relationship between system of weighted variational inequalities and systems of vector
variational inequalities. We define several kinds of weighted monotonicities and establish several existence results for the
solution of the above-mentioned problems under these weighted monotonicities. We introduce also the weighted generalized variational
inequalities over product of sets, that is, weighted variational inequalities for multivalued maps and systems of weighted
generalized variational inequalities. Extensions of weighted monotonicities for multivalued maps are also considered. The
existence of a solution of weighted generalized variational inequalities over product of sets is also studied. The existence
results for a solution of weighted generalized variational inequality problem give also the existence of solutions of systems
of generalized vector variational inequalities.
The first and third author express their thanks to the Department of Mathematical Sciences, King Fahd University of Petroleum
and Minerals, Dhahran, Saudi Arabia for providing excellent research facilities. The authors are also grateful to the referees
for comments and suggestions improving the final draft of this paper. 相似文献