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Zbl 0939.90014
Chen, G.Y.; Goh, C.J.; Yang, X.Q.
Vector network equilibrium problems and nonlinear scalarization methods. (English)
[J] Math. Methods Oper. Res. 49, No.2, 239-253 (1999). ISSN 1432-2994; ISSN 1432-5217/e

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.

MSC 2000:: *90C29 Multi-objective programming, etc.
90C35 Network programming

Keywords: multicriteria network equilibrium; scalarization methods; strictly monotone functions; variational inequalities

Cited in: Zbl 1131.90010

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