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Algorithms for the Split Variational Inequality Problem

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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.

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Authors and Affiliations

  1. Department of Mathematics, University of Haifa, Mt. Carmel, 31905, Haifa, Israel

    Yair Censor

  2. Department of Mathematics, The Technion - Israel Institute of Technology, Technion City, 32000, Haifa, Israel

    Aviv Gibali & Simeon Reich

Authors
  1. Yair Censor
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  2. Aviv Gibali
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  3. Simeon Reich
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Correspondence to Yair Censor.

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Censor, Y., Gibali, A. & Reich, S. Algorithms for the Split Variational Inequality Problem. Numer Algor 59, 301–323 (2012). https://doi.org/10.1007/s11075-011-9490-5

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