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关于一类非线性变分不等式的可解性 被引量：3

On Solvability of a Class of Nonlinear Variational Inequalities
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摘要 在Hilbert空间中引入了一类非线性变分不等式,建立了这类非线性变分不等式近似解的扰动迭代算法,证明了此类非线性变分不等式解的存在性和唯一性,并讨论了由该迭代算法所产生的迭代序列的收敛性. The aim of this paper is to introduce a class of nonlinear variational inequalities in a real Hilbert space. A perturbed iterative algorithm for finding the approximate solutions of the nonlinear variational inequality is suggested. The existence and uniqueness of solution for the nonlinear variational inequality is proved and the convergence of iterative sequence generated by the perturbed iterative algorithm is established.
作者 李劲松
机构地区 铁岭师范高等专科学校
出处 《沈阳师范大学学报（自然科学版）》 CAS 2007年第4期439-441,共3页 Journal of Shenyang Normal University:Natural Science Edition
关键词 非线性变分不等式 扰动迭代算法 收敛性 预解算子 Nonlinear variational inequality perturbed iterative algorithm convergence resolvent operator
分类号 O177.91 [理学—基础数学]
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参考文献5

  • 1ADLY S. Perturbed algorithm and sensitivity analysis for a general class of variational inclusions[J ]. J Math Anal Appl, 1996,201 (3) : 609-630.
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同被引文献22

  • 1CHANG S S,On Chidume's open questions andapproximate solution of multivalued strongly accretive mapping equations in Banach spaces[J].J Math Anal Appl,1997,216(1):94-111.
  • 2BAUOCCHI C,CAPELO A.Variational and quasi-variational inequalities,Application to Free Boundary Problems[M].New York/London:Wiley,1984.
  • 3GIANNESSI F,MAUGERI A.Variational inequalities and network equilibrium problems[M].New York:Plenum,1995.
  • 4GLOWINSKI R,LIONS J L,TTEMOLIERES R.Numerical analysis of variational inequalities[M].Amsterdam:North-Holland,1981.
  • 5GLOWINSKI R.Numerical methods for nonlinear variational problems[M].Berlin:Springer-Verlag,1984.
  • 6HARKER P T,PANG J S.Finite-dimensional variational inequality and nonlinear complementarity problems:a survey of theory,algorithms and applications[J].Math Program,1990,48(1/2/3):161-220.
  • 7HUANG N J.A new completely general class of variational inclusions with noncompact valued mappings[J].Comput Math Appl,1998,35(10):9-14.
  • 8NOOR M A.Some recent advances in variational inequalities,Part Ⅰ,basic concepts[J].New Zeal J Math,1997,26:53 -80.
  • 9DING X P.Perturbed proximal point for generalized quasi variational in clusions[J].J.Math.Anal.Appl,1997,210 (1):88-101.
  • 10KAZMI K R,BHAT M I.Iterative algorithm for a system of nonlinear variational-like inclusions[J].Computers and Mathematics with Applications,2004,48(12):1929-1935.

引证文献3

二级引证文献3

沈阳师范大学学报（自然科学版）
2007年 第4期

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