Vector equilibrium problems with elastic demands and capacity constraints

  • Authors:

  • S. J. Li;K. L. Teo;X. Q. Yang

  • Affiliations:

  • College of Mathematics and Science, Chongqing University, Chongqing, China 400044;Department of Mathematics and Statistics, Curtin University of Technology, Perth, Australia 6845;Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong

  • Venue:
  • Journal of Global Optimization
  • Year:
  • 2007

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Abstract

In this paper, a (weak) vector equilibrium principle for vector network problems with capacity constraints and elastic demands is introduced. A sufficient condition for a (weak) vector equilibrium flow to be a solution for a system of (weak) vector quasi-variational inequalities is obtained. By virtue of Gerstewitz's nonconvex separation functional 驴, a (weak) 驴-equilibrium flow is introduced. Relations between a weak vector equilibrium flow and a (weak) 驴-equilibrium flow is investigated. Relations between weak vector equilibrium flows and two classes of variational inequalities are also studied.