Goh, C. J.; Yang, X. Q. Vector equilibrium problem and vector optimization. (English) Zbl 1009.90093 Eur. J. Oper. Res. 116, No. 3, 615-628 (1999). 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. Cited in 1 ReviewCited in 27 Documents 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 Keywords:vector equilibrium; parametric equilibrium; parametric complementarity problem; vector optimization PDF BibTeX XML Cite \textit{C. J. Goh} and \textit{X. Q. Yang}, Eur. J. Oper. Res. 116, No. 3, 615--628 (1999; Zbl 1009.90093) Full Text: DOI References: [3] Florian, M., Nonlinear cost network models in transportation analysis, Mathematical Programming, 26, 167-196 (1986) · Zbl 0607.90029 [4] Geoffrion, A. M., Proper efficiency and the theory of vector maximization, Journal of Mathematical Analysis and Applications, 22, 618-630 (1968) · Zbl 0181.22806 [7] Leurent, F., Cost versus tiem equilibrium over a network, European Journal of Operational Research, 71, 205-221 (1993) · Zbl 0799.90052 [11] Pang, J. S.; Chan, D., Iterative methods for variational and complementarity problems, Mathematical Programming, 24, 284-313 (1982) · Zbl 0499.90074 [12] Rote, G., The convergence rate of the sandwich algorithm for approximating convex functions, Computing, 48, 337-361 (1992) · Zbl 0787.65006 [14] Smith, M. J., The existence, uniqueness and stability of traffic equilibrium, Transportation Research, 13B, 295-304 (1979) [15] Tung, C. T.; Chew, K. L., A multicriteria Pareto-optimal path algorithm, European Journal of Operational Research, 62, 203-209 (1992) · Zbl 0769.90079 [17] Yang, X. Q., Vector variational inequality and its duality, Nonlinear Analysis, 21, 869-877 (1993) · Zbl 0809.49009 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.