Homotopy Continuous Method for Weak Efficient Solution of Multiobjective Optimization Problem with Feasible Set Unbounded Condition

Show more

References

[1] A. Charne and W. W. Cooper, “Management Models and Industrial Application of Linear Programming,” Wiley Press, New York, 1961.

[2] G. Fandel and T. Gal, “Multiple Criteria Decision Making: Theory and Applications,” Springer-Verlag Press, New York, 1980. doi:10.1007/978-3-642-48782-8

[3] C. B. Garcia and W. I. Zangwill, “Pathways to Solutions, Fixed Points and Equilibria,” Prentice-Hall, Englewood Cliffs, 1981, pp. 475-495.

[4] N. Megiddo, “Pathways to the Optimal Set in Linear Programming,” In: N. Megiddo, Ed., Progress in Mathematical Programming Interior Point and Related Methods, Springer, New York, 1988, pp. 131-158.

[5] M. Kojima, S. Mizuno and A. Yoshise, “A Primal-Dual Interior Point Algorithm for Linear Programming,” In: N. Megiddo, Ed., Progress in Mathematical Programming Interior Point and Related Methods, Springer, New York, 1988, pp. 29-47.

[6] Z. H. Lin, B. Yu and G. C. Feng, “A Combined Homotopy Interior Point Method for Convex Nonlinear Programming Problems,” Applied Mathematics and Computation, Vol. 84, No. 2-3, 1994, pp. 193-211.
doi:10.1016/S0096-3003(96)00086-0

[7] Z. H. Lin, Y. Li and B. Yu, “A Combined Homotopy Interior Point Method for General Nonlinear Programming Problems,” Applied Mathematics and Computation, Vol. 80, No. 2-3, 1997, pp. 209-224.
doi:10.1016/0096-3003(95)00295-2

[8] Z. H. Lin, D. L. Zhu and Z. D. Sheng, “Finding a Minimal Efficient Solution of a Convex Multiobjective Program,” Journal of Optimization Theory and Applications, Vol. 118, No. 3, 2003, pp. 587-600.
doi:10.1023/B:JOTA.0000004872.93803.09

[9] W. Song and G. M. Yao, “Homotopy Method for a General Multiobjective Programming Problem,” Journal of Optimization Theory and Applications, Vol. 138, No. 1, 2008, pp. 139-153. doi:10.1007/s10957-008-9366-6

[10] T. Maeda, “Second-Order Conditions for Efficiency Nonsmooth Multiobjective Optimization Problems,” Journal of Optimization Theory and Applications, Vol. 122, No. 3, 2004, pp. 521-538.
doi:10.1023/B:JOTA.0000042594.46637.b4

[11] L. T. Watson, “Globally Convergent Homotopy Algorithms for Nonlinear Systems of Equations,” Nonlinear Dynamics, Vol. 1, No. 2, 1990, pp.143-191.
doi:10.1007/BF01857785

[12] G. C. Feng, Z. L. Lin and B. Yu, “Existence of an Interior Pathway to a Karush-Kuhn-Tucker Point of a Nonlinear Programming Problem,” Nonlinear Analysis, Vol. 32, No. 6, 1998, pp. 761-768.
doi:10.1016/S0362-546X(97)00516-6

[13] Q. Xu, B. Yu and G. C. Feng, “Homotopy Methods for Solving Variational Inequalities in Unbounded Sets,” Journal of Global Optimization, Vol. 31, No. 1, 2005, pp. 121-131. doi:10.1007/s10898-004-4272-4

[14] Q. Xu, B. Yu, G. C. Feng and C. Y. Dan, “Condition for Global Convergence of a Homotopy Method for Variational Inequality Problems on Unbounded Sets,” Optimization Methods and Software, Vol. 22, No. 4, 2007, pp. 587-599. doi:10.1080/10556780600887883

[15] C. Y. Lin and J. L. Dong, “Methods and Theories in Multiobjective Optimization,” Jilin Education Press, Changchun, 1992.

[16] H. W. Kuhn and A. W. Tucker, “Nonlinear Programming,” Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, University of California Press, Berkeley, 1951.

[17] G. L. Naber, “Topological Methods in Euclidean Space,” Cambridge University Press, London, 1980.