Algorithms for the Split Variational Inequality Problem View Full Text


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Article Info

DATE

2012-02

AUTHORS

Yair Censor, Aviv Gibali, Simeon Reich

ABSTRACT

We propose a prototypical Split Inverse Problem (SIP) and a new variational problem, called the Split Variational Inequality Problem (SVIP), which is a SIP. It entails finding a solution of one inverse problem (e.g., a Variational Inequality Problem (VIP)), the image of which under a given bounded linear transformation is a solution of another inverse problem such as a VIP. We construct iterative algorithms that solve such problems, under reasonable conditions, in Hilbert space and then discuss special cases, some of which are new even in Euclidean space. More... »

PAGES

301-323

References to SciGraph publications

  • 2011-02. The Subgradient Extragradient Method for Solving Variational Inequalities in Hilbert Space in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 2006-01. Weak Convergence Theorem by an Extragradient Method for Nonexpansive Mappings and Monotone Mappings in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 2011. Opial-Type Theorems and the Common Fixed Point Problem in FIXED-POINT ALGORITHMS FOR INVERSE PROBLEMS IN SCIENCE AND ENGINEERING
  • 2003-08. Weak Convergence Theorems for Nonexpansive Mappings and Monotone Mappings in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 1994-09. A multiprojection algorithm using Bregman projections in a product space in NUMERICAL ALGORITHMS
  • 1984-01. Decomposition through formalization in a product space in MATHEMATICAL PROGRAMMING
  • 2012-06. Common Solutions to Variational Inequalities in SET-VALUED AND VARIATIONAL ANALYSIS
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    http://scigraph.springernature.com/pub.10.1007/s11075-011-9490-5

    DOI

    http://dx.doi.org/10.1007/s11075-011-9490-5

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