| Hilbert空间中关于松弛协强制映射的广义变分不等式组 |
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| 引用本文： | 张玉敏,张国春,刘英.Hilbert空间中关于松弛协强制映射的广义变分不等式组[J].河北大学学报(自然科学版),2012,32(5):453-457. |
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| 作者姓名： | 张玉敏 张国春 刘英 |
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| 作者单位： | 1. 河北金融学院 管理系,河北保定,071051
2. 河北大学 数学与计算机学院,河北保定,071002 |
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| 基金项目： | 国家自然科学基金资助项目(11101115);河北省自然科学基金资助项目(A2011201053) |
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| 摘 要： | 引入了一类新的关于松驰协强制映射的广义变分不等式组,通过用度量投影的方法证明了这类广义变分不等式组解的存在性和唯一性,而且建立了一类新的算法来逼近这一不等式组的解,同时讨论了该算法的收敛性,使得近期相关结果成为所得结果的特殊情况.
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| 关 键 词： | 松驰协强制性映射 广义变分不等式组 度量投影 Lipschitz连续 Mann-迭代 |
System of generalized variational inequalities for relaxed cocoercive mappings in Hilbert spaces |
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| ZHANG Yumin
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ZHANG Guochun
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LIU Ying.System of generalized variational inequalities for relaxed cocoercive mappings in Hilbert spaces[J].Journal of Hebei University (Natural Science Edition),2012,32(5):453-457. |
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| Authors: | ZHANG Yumin ZHANG Guochun LIU Ying |
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| Institution: | 1.Department of Management,Hebei Finance University,Baoding 071001,China; 2.College of Mathematics and Computer Science,Hebei University,Baoding 071002,China) |
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| Abstract: | A new system of generalized variational inequalities involving relaxed cocoercive mappings in Hilbert space are introduced.By using the projection method,the existence and uniqueness of solutions for this new system of generalized variational inequalities are proved.Furthermore,a new algorithm for approximating the solution of this system is constructed and the convergence of the iterative sequence generated by the algorithm is discussed. |
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| Keywords: | relaxed cocoercive mapping system of generalized variational inequalities metric projection Lipschitz-continuity Mann-iteration |
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