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Relaxed Quasimonotone Operators and Relaxed Quasiconvex Functions

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Abstract

In this paper, we introduce the class of multivalued relaxed μ quasimonotone operators and establish the existence of solutions of variational inequalities for such operators. This result is compared with a recent result of Bai et al. on densely relaxed pseudomonotone operators. A similar comparison regarding an existence result of Luc on densely pseudomonotone operators is provided. Also, we introduce a broad class of functions, called relaxed quasiconvex functions, and show that they are characterized by the relaxed μ quasimonotonicity of their subdifferentials. The results strengthen a variety of other results in the literature.

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Authors and Affiliations

  1. College of Mathematics and Econometrics, Hunan University, Changsha, Hunan, 410082, China

    M. R. Bai

  2. Department of Product and Systems Design Engineering, University of the Aegean, Hermoupolis, Syros, 84100, Greece

    N. Hadjisavvas

Authors
  1. M. R. Bai
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  2. N. Hadjisavvas
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Corresponding author

Correspondence to N. Hadjisavvas.

Additional information

Communicated by S. Schaible.

This work is supported by NNSF of China (10571046) and by the GSRT of Greece (06FR-062).

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Bai, M.R., Hadjisavvas, N. Relaxed Quasimonotone Operators and Relaxed Quasiconvex Functions. J Optim Theory Appl 138, 329–339 (2008). https://doi.org/10.1007/s10957-008-9382-6

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  • DOI: https://doi.org/10.1007/s10957-008-9382-6

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