Solvability of variational inequalities on Hilbert lattices

Hiroki Nishimura, Ahmet Ok

    Research output: Contribution to journalArticle

    Abstract

    This paper provides a systematic solvability analysis for (generalized) variational inequalities on separable Hilbert lattices. By contrast to a large part of the existing literature, our approach is lattice-theoretic, and is not based on topological fixed point theory. This allows us to establish the solvability of certain types of (generalized) variational inequalities without requiring the involved (set-valued) maps be hemicontinuous or monotonic. Some of our results generalize those obtained in the context of nonlinear complementarity problems in earlier work, and appear to have scope for applications. This is illustrated by means of several applications to fixed point theory, optimization, and game theory.

    Original languageEnglish (US)
    Pages (from-to)608-625
    Number of pages18
    JournalMathematics of Operations Research
    Volume37
    Issue number4
    DOIs
    StatePublished - Nov 2012

    Fingerprint

    Generalized Variational Inequality
    Fixed Point Theory
    Variational Inequalities
    Hilbert
    Solvability
    Nonlinear Complementarity Problem
    Optimization Theory
    Set-valued Map
    Game theory
    Game Theory
    Monotonic
    Generalise
    Fixed point
    Variational inequalities
    Context
    Nonlinear complementarity problem

    Keywords

    • Fixed point theorems
    • Hilbert lattices
    • Variational inequalities

    ASJC Scopus subject areas

    • Mathematics(all)
    • Computer Science Applications
    • Management Science and Operations Research

    Cite this

    Solvability of variational inequalities on Hilbert lattices. / Nishimura, Hiroki; Ok, Ahmet.

    In: Mathematics of Operations Research, Vol. 37, No. 4, 11.2012, p. 608-625.

    Research output: Contribution to journalArticle

    Nishimura, Hiroki ; Ok, Ahmet. / Solvability of variational inequalities on Hilbert lattices. In: Mathematics of Operations Research. 2012 ; Vol. 37, No. 4. pp. 608-625.
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