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Vector equilibrium problems with elastic demands and capacity constraints. (English) Zbl 1143.90387
The authors study a vector network equilibrium problem with capacity constraints and elasticity demands. They use a particular nonconvex separation functional (called Gerstewitz’s functional) to scalarize the problem and prove an equivalence between the vector problems and the scalarized ones. It is to note that Gerstewitz’s functional is known also as the smallest monotonic function in the literature, and it can be found in earlier works by A. M. Rubinov [Sib. Mat. Zh. 17, 370–380 (1976; Zbl 0331.46013)] or by A. Pascoletti and P. Serafini [J. Optimization Theory Appl. 42, 499–524 (1984; Zbl 0505.90072)].
90C29Multi-objective programming; goal programming
90C47Minimax problems
[1]Chen, G.Y., Yen, N.D.: On the variational inequality model for network equilibrium. Internal Report 3.196 (724), Department of Mathematics, University of Pisa, Pisa (1993).
[2]Chen G.Y., Goh C.J., Yang X.Q. (1999). Vector network equilibrium problems and nonlinear scalarization methods. Math. Methods Oper. Res. 49:239–253
[3]Cheng, T.C.E., Wu, Y.N.: A multiclass, multicriteria supply-demand network equilibrium model, preprint
[4]Daniele P., Maugeri A. (2002). Variational inequalities and discrete and continuum models of network equilibrium problems. Math. Comput. Model 35:689–708 · Zbl 0994.90033 · doi:10.1016/S0895-7177(02)80030-9
[5]Daniele P., Maugeri A., Oettli W. (1999). Time-dependent traffic equilibria. J. Optim. Theory Appl. 103:543–555 · Zbl 0937.90005 · doi:10.1023/A:1021779823196
[6]Daniele P., Maugeri A., Oettli W. (1998). Variational inequalities and time-dependent traffic equilibria. C. R. Acad. Sci. Paris Sér. I Math. 326:1059–1062
[7]Gerth C., Weidner P. (1990). Nonconvex separation theorems and some applications in vector optimization. J. Optim. Theory Appl. 67:297–320 · Zbl 0692.90063 · doi:10.1007/BF00940478
[8]Giannessi, F., Maugeri, A.: Variational inequalities and network equilibrium problems. In: Proceedings of the Conference Held in Erice, Plenum Press, New York 1994
[9]Giannessi F. (2000). Vector Variational Inequalities and Vector Equilibria. Kluwer Academic Publisher, Dordrecht
[10]Goh C.J., Yang X.Q. (1999). Theory and methodology of vector equilibrium problem and vector optimization. Eur. J. Oper. Res. 116:615–628 · Zbl 1009.90093 · doi:10.1016/S0377-2217(98)00047-2
[11]Li, S.J., Teo, K.L., Yang, X.Q.: A remark on a standard and linear vector network equilibrium problem with capacity constraints. Eur. J. Oper. Res. (online)
[12]Mageri A. (1995). Variational and quasi-variational inequalities in network flow models. In: Giannessi F., Maugeri A. (eds) Recent developments in theory and algorithms, Variational inequalities and network equilibrium problems. Plenum Press, New York, pp. 195–211
[13]Nagurney A. (1999). Network Economics, A Variational Inequality Approach. Kluwer Academic Publishers, Dordrecht
[14]Nagurney A. (2000). A multiclass, multicriteria traffic network equilibrium model. Math. Comp. Model. 32:393–411 · Zbl 0965.90003 · doi:10.1016/S0895-7177(00)00142-4
[15]Nagurney A., Dong J. (2002). A multiclass, multicriteria traffic network equilibrium model with elastic demand. Transpor. Res. Part B 36:445–469 · doi:10.1016/S0191-2615(01)00013-3
[16]Yang X.Q., Goh C.J. (1997). On vector variational inequalities: application to vector equilibria. J. Optim. Theory Appl. 95:431–443 · Zbl 0892.90158 · doi:10.1023/A:1022647607947