Super Efficiency of Multicriterion Network Equilibrium Model and Vector Variational Inequality

The super efficiency of a vector variational inequality is considered in this paper. We show that for both the single and multiple criteria cases, a network equilibrium model can be recast as super efficient solutions to a kind of variational inequality. For the network equilibrium model with a vector-valued cost function, we derive the necessary and sufficient condition in terms of the super efficiency of a vector variational inequality by using the Gerstewitz’s function without any convex assumptions.

[1]  Dimitri P. Bertsekas,et al.  Nonlinear Programming , 1997 .

[2]  S. J. Li,et al.  Semicontinuity of the solution set map to a set-valued weak vector variational inequality , 2007 .

[3]  G. Chen.  Existence of solutions for a vector variational inequality: An extension of the Hartmann-Stampacchia theorem , 1992 .

[4]  A. M. Geoffrion.  Proper efficiency and the theory of vector maximization , 1968 .

[5]  X. Q. Yang,et al.  Vector network equilibrium problems and nonlinear scalarization methods , 1999, Math. Methods Oper. Res..

[6]  J. Borwein.  Proper Efficient Points for Maximizations with Respect to Cones , 1977 .

[7]  M. I. Henig.  Proper efficiency with respect to cones , 1982 .

[8]  Yunan Wu,et al.  Henig efficiency of a multi-criterion supply-demand network equilibrium model , 2006 .

[9]  Wei Liu,et al.  Proper efficiency for set-valued vector optimization problems and vector variational inequalitiesRID="*"ID="*"  This research was partially supported by the National Natural Science Foundation of P.R. China and the Natural Science Foundation of Jiangxi Province, P.R. China. , 2000, Math. Methods Oper. Res..

[10]  J. Borwein,et al.  Super efficiency in vector optimization , 1993 .

[11]  Xiaoqi Yang,et al.  On Vector Variational Inequalities: Application to Vector Equilibria , 1997 .

[12]  Xiaoqi Yang,et al.  Vector variational-like inequality with pseudoinvexity , 2006 .

[13]  W. R. Buckland,et al.  Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability. , 1952 .

[14]  J. G. Wardrop,et al.  Some Theoretical Aspects of Road Traffic Research , 1952 .

[15]  Xiao-Li Hu,et al.  Optimal Adaptive Regulation for Nonlinear Systems with Observation Noise , 2007 .

[16]  K. Schittkowski,et al.  NONLINEAR PROGRAMMING , 2022 .

[17]  C. Gerth,et al.  Nonconvex separation theorems and some applications in vector optimization , 1990 .

[18]  Kok Lay Teo,et al.  A remark on a standard and linear vector network equilibrium problem with capacity constraints , 2008, Eur. J. Oper. Res..

[19]  A. Nagurney.  Network Economics: A Variational Inequality Approach , 1992 .

[20]  H. P. Benson,et al.  An improved definition of proper efficiency for vector maximization with respect to cones , 1979 .