INFORMATION CHANGE THE WORLD

International Journal of Image, Graphics and Signal Processing(IJIGSP)

ISSN: 2074-9074 (Print), ISSN: 2074-9082 (Online)

Published By: MECS Press

IJIGSP Vol.3, No.2, Mar. 2011

The Aggregate Homotopy Method for Multi-objective Max-min Problems

Full Text (PDF, 189KB), PP.30-36


Views:59   Downloads:0

Author(s)

He Li,Dong Xiao-gang,Tan Jia-wei,Liu Qing-huai

Index Terms

Multi-objective optimization, homotopy method, aggregate function

Abstract

Multi-objective programming problem was transformed into a class of simple unsmooth single-objective programming problem by Max-min ways. After smoothing with aggregate function, a new homotopy mapping was constructed. The minimal weak efficient solution of the multi-objective optimization problem was obtained by path tracking. Numerical simulation confirmed the viability of this method.

Cite This Paper

He Li,Dong Xiao-gang,Tan Jia-wei,Liu Qing-huai,"The Aggregate Homotopy Method for Multi-objective Max-min Problems", IJIGSP, vol.3, no.2, pp.30-36, 2011.

Reference

[1]R. B. Kellogg, T. Y. Li , J. A. Yorke, A constructive proof of the Brouwer fixed-point theorem and computational results, SIAM J. Numer. Anal., 18(1976),473-483.

[2]S. N. Chow,J. Mallet-Paret ,J. A. yorke, Finding zero of maps: Homotopy methods that are constructive with probanility one, Math.Comput., 32(1978),887-899.

[3]N. Megiddo, Pathways to the optimal set in linear programming, in Progress in Mathematical Programming, Interior Point and Related Methods, (N. Megiddo, Ed.), Springer, New York, 1988, pp. 131-158.

[4]M. Kojima, S. Mizuno, A. Yoshise, A primal-dual interior point algorithm for linear programming, in Progress in Mathematical Programming, Interior Point and Related Methods (N. Megiddo, Ed.), Springer, New York, 1988, pp. 29-47.

[5]Z. H. Lin, B. Yu and G. C. Feng , A combined homotopy interior method for convex nonlinear programming, Appl. Math. Comput. 84(1997), 93-211.

[6]Z. H. Lin, Y. Li, and B. Yu, A combined homotopy interior point method for general nonlinear programming problems,Appl. Math. Comput, 80(1996), 209–224 .

[7]Q. H. Liu, B. Yu, G. C. Feng, An interior point path-following method for nonconvex programming with quasi normal cone condition, Advances in Mathematics, 29(2000), 281-282.

[8]B.Yu, Q. H. Liu, G. C. Feng, A combined homotopy interior point method for nonconvex programming with pseudo cone condition, Northeast. Math. J., 16(2000), 383-386.

[9]Z.H.Lin,D.L.Zhu,Z.P.Sheng,Finding a Minimal Efficient Solution of a Convex Multiobjective Program,Journal of Oprimization Theory and Applications, 118(2003), 587-600.

[10]C. Y. Lin, J. L. Dong, Multi-objective Optimization Theory and Method. [M], Changchun, Jilin Teaching Press, 1992.

[11]X. S. Li, Aggregate Funtion Method for solving of nonlinear programming, Chinese Science (A), 12(1991), 1283-1288.

[12]B. Yu, G. C. Feng, S. L. Zhang, The Aggregate Constraint Homotopy Method for Nonconvex Nonlinear Programming. J. Nonlinear Analysis, 45(2001), 839–847.

[13]Zhang, Z.S.: Introduction to Differential Topology. Beijing University Press, Beijing (2002) (in Chinese)

[14]Naber, G.L.: Topological Methods in Euclidean Spaces. Cambridge University Press, London (1980)

[15]Q. H. Liu, A Combined Homotopy Interior-point for Solving Nonconvex Programming Problem. [D].Changchun, Jilin University, 1999(in Chinese)

[16]E. L. Allgower and K. Georg, Numerical Continuation Methods: An Introduction, Springer-Verlag, Berlin, New York, 1990.

[17]C. B. Garcia, W. I. Zangwill, Pathways to Solutions, Fixed Points and Equilibria, Prentice-Hall, New Jersey, 1981.