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An Extension of Pseudolinear Functions and Variational Inequality Problems

Author

Listed:
  • M. Bianchi

    (Catholic University)

  • S. Schaible

    (University of California)

Abstract

In optimization, objective functions which are both pseudoconvex and pseudoconcave have been studied extensively. Generalizing these results, we characterize pseudomonotone maps F where -F is also pseudomonotone and explore their properties in variational inequality problems. In particular, we extend recent results by Jeyakumar and Yang which were derived for optimization problems.

Suggested Citation

  • M. Bianchi & S. Schaible, 2000. "An Extension of Pseudolinear Functions and Variational Inequality Problems," Journal of Optimization Theory and Applications, Springer, vol. 104(1), pages 59-71, January.
    • Handle: RePEc:spr:joptap:v:104:y:2000:i:1:d:10.1023_a:1004672604998
    DOI: 10.1023/A:1004672604998
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    References listed on IDEAS

    as
    1. Komlosi, S., 1993. "First and second order characterizations of pseudolinear functions," European Journal of Operational Research, Elsevier, vol. 67(2), pages 278-286, June.
    2. Rapcsak, T., 1991. "On pseudolinear functions," European Journal of Operational Research, Elsevier, vol. 50(3), pages 353-360, February.
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    Cited by:

    1. Vsevolod I. Ivanov, 2013. "Optimality Conditions and Characterizations of the Solution Sets in Generalized Convex Problems and Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 158(1), pages 65-84, July.
    2. T. Rapcsák & M. Ujvári, 2008. "Some results on pseudolinear quadratic fractional functions," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 16(4), pages 415-424, December.
    3. John Cotrina & Michel Théra & Javier Zúñiga, 2020. "An Existence Result for Quasi-equilibrium Problems via Ekeland’s Variational Principle," Journal of Optimization Theory and Applications, Springer, vol. 187(2), pages 336-355, November.
    4. N. T. H. Linh & J.-P. Penot, 2012. "Generalized Affine Functions and Generalized Differentials," Journal of Optimization Theory and Applications, Springer, vol. 154(2), pages 321-338, August.

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