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  • Research Article
  • Open Access

An Algorithm Based on Resolvant Operators for Solving Positively Semidefinite Variational Inequalities

Fixed Point Theory and Applications20072007:076040

  • Received: 16 June 2007
  • Accepted: 19 September 2007
  • Published:


A new monotonicity, -monotonicity, is introduced, and the resolvant operator of an -monotone operator is proved to be single-valued and Lipschitz continuous. With the help of the resolvant operator, the positively semidefinite general variational inequality (VI) problem VI is transformed into a fixed point problem of a nonexpansive mapping. And a proximal point algorithm is constructed to solve the fixed point problem, which is proved to have a global convergence under the condition that in the VI problem is strongly monotone and Lipschitz continuous. Furthermore, a convergent path Newton method is given for calculating -solutions to the sequence of fixed point problems, enabling the proximal point algorithm to be implementable.


  • Variational Inequality
  • Differential Geometry
  • Computational Biology
  • Resolvant Operator


Authors’ Affiliations

Department of Applied Mathematics, Dalian University of Technology, Dalian, Liaoning, 116024, China


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© Juhe Sun et al. 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.