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

2014 ◽  
Vol 93 (10) ◽  
pp. 2199-2210 ◽  
Author(s):  
Y.D. Xu ◽  
S.J. Li
Keyword(s):  
Equilibrium Problems ◽  
Capacity Constraints ◽  
Network Equilibrium ◽  
Nonlinear Scalarization ◽  
Scalarization Methods ◽  
Network Equilibrium Problems

scholarly journals Traffic Network Equilibrium Problems with Capacity Constraints of Arcs and Linear Scalarization Methods

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
X. Q. Tian ◽  
Y. D. Xu
Keyword(s):  
Equilibrium Problems ◽  
Sufficient Conditions ◽  
Capacity Constraints ◽  
Network Equilibrium ◽  
Traffic Network ◽  
Equilibrium Flow ◽  
Traffic Network Equilibrium ◽  
Vector Equilibrium ◽  
Network Equilibrium Problems ◽  
Weak Vector

Traffic network equilibrium problems with capacity constraints of arcs are studied. A (weak) vector equilibrium principle with vector-valued cost functions, which are different from the ones in the work of Lin (2010), and three kinds of parametric equilibrium flows are introduced. Some necessary and sufficient conditions for a (weak) vector equilibrium flow to be a parametric equilibrium flow are derived. Relationships between a parametric equilibrium flow and a solution of a scalar variational inequality problem are also discussed. Some examples are given to illustrate our results.

A Nonlinear Equation Framework for Solving Network Equilibrium Problems

1984 ◽  
Vol 16 (1) ◽  
pp. 67-80 ◽  
Author(s):  
C Fisk
Keyword(s):  
Existence And Uniqueness ◽  
Equilibrium Problems ◽  
Iterative Solution ◽  
System Of Nonlinear Equations ◽  
Network Equilibrium ◽  
Convergence Properties ◽  
Equilibrium Conditions ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Network Equilibrium Problems

The author presents a general framework for formulating network equilibrium problems in which the equilibrium conditions are given by a system of nonlinear equations. Existence and uniqueness results are presented, and iterative solution techniques with well-defined convergence properties are suggested. For illustrative purposes, these techniques are applied to a specific two-mode equilibrium model; a discussion comparing some aspects of this approach with other existing approaches is included.

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