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Symmetric duality in multi-objective programming

Published online by Cambridge University Press:  17 February 2009

S. Chandra  and
M. V. Durga Prasad
S. Chandra
Affiliation:
Dept of Mathematics, Indian Institute Technology, Hauz Khas, New Delhi-110016, India.
M. V. Durga Prasad
Affiliation:
Dept of Mathematics, Karnataka Regional Engineering College, Surathkal-574157, India.
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Abstract

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A pair of multi-objective programming problems is shown to be symmetric dual by associating a vector-valued infinite game to the given pair. This symmetric dual pair seems to be more general than those studied in the literature.

Type
Research Article
Information
The ANZIAM Journal , Volume 35 , Issue 2 , October 1993 , pp. 198 - 206
Copyright
Copyright © Australian Mathematical Society 1993

References

[1]Corley, H. W., “Games with vector pay-offs”, Journal of Optimization theory and applications 47 (1985) 491–498.CrossRefGoogle Scholar
[2]Cottle, R. W., “An infinite game with a convex-concave pay-off kernel”, Research Report No. ORC 63–19 (RN-2), Operations Research Centre, University of California, Berkley, 1963, unpublished.Google Scholar
[3]Craven, B. D., “Lagrangian conditions and quasi-duality”, Bull. Aust. Math. Soc. 16 (1977) 325–339.CrossRefGoogle Scholar
[4]Craven, B. D., “Lagrangian conditions, vector minimization and local duality”, Research Report No. 37, Department of Mathematics, University of Melbourne, Australia, 1980.CrossRefGoogle Scholar
[5]Dantzig, G. B., Eisenberg, E. and Cottle, R. W., “Symmetric dual nonlinear programs”, Pacific J. Math. 15 (1965) 809–812.CrossRefGoogle Scholar
[6]Dorn, W. S., “A symmetric dual theorem for quadratic programs”, Journal of Operations Research Society of Japan 2 (1960) 93–97.Google Scholar
[7]Mond, B., “A symmetric dual theorem for nonlinear programs”, Quart. of Appl. Math. 23 (1965) 265–269.CrossRefGoogle Scholar
[8]Mond, B., “A symmnetric duality for nonlinear programming”, OPSEARCH 13 (1976) 1–10.Google Scholar
[9]Mond, B. and Weir, T., “Generalized concavity and duality”, in Generalized Concavity in Optimization and Economics (eds. Schaible, S. and Zeimba, W. T.), (Academic Press, 1981) 263–279.Google Scholar
[10]Rödder, W., “A generalized saddle point theory: its application to duality theory for linear vector optimum problems”, European Journal of Operations Research (1977) 55–59.CrossRefGoogle Scholar
[11]Singh, C., “Optimality conditions in multiobjective differentiable programming”, Journal of Optimization Theory and Applications 53 (1987) 115–123.CrossRefGoogle Scholar
[12]Tanino, T., Sawaragi, Y. and Nakayama, A., Theory of Multiobjective Optimizations (Academic Press, Inc, USA, 1985).Google Scholar
[13]Weir, T. and Mond, B., “Symmetric and self duality in multiobjective programming”, Asia Pacific Journal of Operational Research 5 (2) (1988) 124–133.Google Scholar