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Vector equilibrium problem and vector optimization. (English) Zbl 1009.90093

Summary: This paper examines the vector equilibrium model based on a vector cost consideration. This is a generalization of the well-known Wardrop traffic equilibrium principle where road users choose paths based on just a single cost. The concept of parametric equilibria is introduced and used to establish relations with parametric complementarity and variational inequality problems. Relations with some vector optimization problems via scalarization techniques are given under appropriate conditions. Some solution methods for solving vector equilibrium problems are also discussed.

MSC:

90C27 Combinatorial optimization
90B20 Traffic problems in operations research
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
90C31 Sensitivity, stability, parametric optimization
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