Vector network equilibrium problems with capacity constraints of arcs and nonlinear scalarization methods

Abstract

In this paper, a vector network equilibrium problem with capacity constraints of arcs is studied. By virtue of Fan-Browder’ fixed point theorem, an existence result of a (weak) vector equilibrium flow is derived. By using nonlinear scalarization methods, some sufficient and necessary conditions for a weak vector equilibrium flow are obtained.

Keywords:

• vector traffic network equilibrium problem
• vector equilibrium flow
• -equilibrium flow
• nonlinear scalarization method
• variational inequality

AMS Subject Classifications:

• 90B105
• 90B20
• 49J40

Acknowledgments

The authors would like to thank the anonymous reviewers for their valuable comments and suggestions, which helped to improve the paper.