Error Estimation for a Economic Equilibrium Modeling

Abstract:

In this paper, the global error estimation for the generalized linear complementarity problem in economic equilibrium modeling(GLCP) is established. The result obtained in this paper can be viewed as extensions of previously known results.

• Periodical: Advanced Materials Research (Volume 267)
• Pages: 350-355
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.267.350
• Online since: June 2011
• Authors: Lei Wang
• Keywords: Economic Modeling, Error Estimation, Generalized Linear Complementarity Problem

References

[1] M.C. Ferris and J.S. Pang: Engineering and economic applications of complementarity problems. Society for industrial and applied mathematics, 39(4) (1997), pp.669-713.

[2] L. Walras: Elements of Pure Economics,. Allen and Unwin, London, (1954).

[3] A. Nagurney, J. Dong, D. Zhang: A supply chain network equilibrium model. Transportation Research. Part E 38(2002), p.281.

DOI: 10.1016/s1366-5545(01)00020-5

[4] L.P. Zhang: A nonlinear complementarity model for supply chain network equilibrium. Journal of Industrial and Managment Optimization. 3(4) (2007), pp.727-737.

[5] F. Facchinei and J.S. Pang: Finite-Dimensional Variational Inequality and Complementarity Problems, Springer, New York, (2003).

[6] J.S. Pang: Error bounds in mathematical programming. Math. Programming. 79(1997), pp.299-332.

DOI: 10.1007/bf02614322

[7] M.V. Solodov: Convergence rate analysis of iteractive algorithms for solving variational inequality problems. Math. Programming. Ser. A 96(2003), pp.513-528.

DOI: 10.1007/s10107-002-0369-z

[8] Z.Q. Luo, Mangasarian O.L., Ren J. and Solodov M.V.: New error bound for the linear complementarity problem. Mathematics of Operations Research. 19(1994), pp.880-892.

DOI: 10.1287/moor.19.4.880

[9] O.L. Mangasarian and J. Ren: New improved error bound for the linear complementtarity problem. Math. Programming. 66(1994), pp.241-255.

DOI: 10.1007/bf01581148

[10] Mangasarian O.L. and Shiau T.H.: Error bounds for monotone linear complementarity problems. Math. Programming. 36(1) (1986), pp.81-89.

DOI: 10.1007/bf02591991

[11] O.L. Mangasarian: Error bounds for nondegenerate monotone linear complementarity problems. Math. Programming. 48(1990), pp.437-445.

DOI: 10.1007/bf01582267

[12] R. Mathias and J.S. Pang: Error bound for the linear complementarity problem with a P-matrix. linear Algebra and Applications. 132(1990), pp.123-136.

DOI: 10.1016/0024-3795(90)90058-k

[13] B. Chen, Error Bounds for -Type and Monotone Nonlinear Complementarity Problems, J. Optim. Theory Appl., 108(2) (2001), pp.297-316.

DOI: 10.1023/a:1026434200384

[14] N.H. Xiu, J.Z. Zhang, Global Projection-Type Error Bound for General Variational Inequalities, J. Optim. Theory Appl., 112(1) (2002), pp.213-228.

DOI: 10.1023/a:1013056931761

[15] H.C. Sun, Y.J. Wang, L.Q. Qi: Global Error Bound for the Generalized Linear Complementarity Problem over a Polyhedral Cone. J. Optim. Theory Appl. 142(2009), p.417—429.

DOI: 10.1007/s10957-009-9509-4

[16] A.J. Hoffman, on the approximate solutions of linear inequalities, J. Res. National Bureau of Standards, 49 (1952), pp.263-265.

DOI: 10.6028/jres.049.027

[17] Z. Q. Luo, J. F. Sturm, Error bound for quadratic systems, http: /citeseerx. ist. psu. edu/viewdoc/summary?doi=10. 1. 1. 56. 3474.

[18] Y.J. Wang, N.H. Xiu, Theory and algorithms for nonlinear programming, Shanxi science and technology press, (2004) pp.170-171 (In Chinese).