方长杰.非线性混合似变分不等式的扰动近似点-投影算法[J].数学研究及应用,2010,30(1):127~140
非线性混合似变分不等式的扰动近似点-投影算法
Perturbed Proximal-Projection Methods for Nonlinear Mixed Variational-Like Inequalities
投稿时间:2007-11-29  最后修改时间:2008-07-07
DOI:10.3770/j.issn:1000-341X.2010.01.012
中文关键词:  非线性混合似变分不等式  扰动近似点-投影算法  公共元素  非扩张映射  松弛$(\gamma, r)$-余强制映射.
英文关键词:nonlinear mixed variational-like inequalities  perturbed proximal-projection methods  common elements  nonexpansive mappings  relaxed $(\gamma,r)$-cocoercive mappings.
基金项目:重庆市科委自然科学基金计划项目(No. 2008BB7415); 重庆邮电大学自然科学基金项目(No. A2008-47).
作者单位
方长杰 重庆邮电大学应用数学研究所, 重庆 400065 
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中文摘要:
      引入了求解非线性混合似变分不等式的扰动近似点-投影算法, 证明了由算法所生成迭代序列强收敛于非扩张映射不动点集合与非线性混合似变分不等式解集合的公共元素.方法和结果是新的, 且推广了这一领域内许多已知结果.
英文摘要:
      In this paper we introduce a new perturbed proximal-projection algorithm for finding the common element of the set of fixed points of non-expansive mappings and the set of solutions of nonlinear mixed variational-like inequalities. The convergence criteria of the iterative sequences generated by the new iterative algorithm is also given. Our approach and results generalize many known results in this field.
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