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Gap functions for a system of generalized vector quasi-equilibrium problems with set-valued mappings

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Abstract

In this paper, some gap functions for three classes of a system of generalized vector quasi-equilibrium problems with set-valued mappings (for short, SGVQEP) are investigated by virtue of the nonlinear scalarization function of Chen, Yang and Yu. Three examples are then provided to demonstrate these gap functions. Also, some gap functions for three classes of generalized finite dimensional vector equilibrium problems (GFVEP) are derived without using the nonlinear scalarization function method. Furthermore, a set-valued function is obtained as a gap function for one of (GFVEP) under certain assumptions.

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Authors and Affiliations

  1. Department of Mathematics, Sichuan University, Chengdu, Sichuan, 610064, P.R. China

    Nan-jing Huang

  2. School of Mathematics and Information, China West Normal University, Nanchong, Sichuan, 637002, P.R. China

    Jun Li

  3. Institute of Applied Mathematics, National Cheng-Kung University, Tainan, 700, Taiwan

    Soon-yi Wu

  4. National Center for Theoretical Sciences, Tainan, Taiwan

    Soon-yi Wu

Authors
  1. Nan-jing Huang
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  2. Jun Li
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  3. Soon-yi Wu
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Correspondence to Soon-yi Wu.

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Huang, Nj., Li, J. & Wu, Sy. Gap functions for a system of generalized vector quasi-equilibrium problems with set-valued mappings. J Glob Optim 41, 401–415 (2008). https://doi.org/10.1007/s10898-007-9248-8

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  • DOI: https://doi.org/10.1007/s10898-007-9248-8

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