Chen, G. Y.; Goh, C. J.; Yang, X. Q. Vector network equilibrium problems and nonlinear scalarization methods. (English) Zbl 0939.90014 Math. Methods Oper. Res. 49, No. 2, 239-253 (1999). Summary: The conventional equilibrium problem found in many economics and network models is based on a scalar cost, or a single objective. Recently, equilibrium problems based on a vector cost, or multicriteria, have received considerable attention. In this paper, we study a scalarization method for analyzing network equilibrium problems with vector-valued cost function. The method is based on a strictly monotone function originally proposed by Gerstewitz. Conditions that are both necessary and sufficient for weak vector equilibrium are derived, with the prominent feature that no convexity assumptions are needed, in contrast to other existing scalarization methods. Cited in 1 ReviewCited in 30 Documents MSC: 90C29 Multi-objective and goal programming 90C35 Programming involving graphs or networks Keywords:multicriteria network equilibrium; scalarization methods; strictly monotone functions; variational inequalities PDFBibTeX XMLCite \textit{G. Y. Chen} et al., Math. Methods Oper. Res. 49, No. 2, 239--253 (1999; Zbl 0939.90014)