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Multiobjective symmetric duality with invexity

Published online by Cambridge University Press:  17 April 2009

T.R. Gulati
Affiliation:
School of Basic & Applied SciencesThapar Institute of Engineering & TechnologyPatiala - 147 001India
I. Husain
Affiliation:
Department of MathematicsRegional Engineering CollegeHazratbal, Srinagar - 190 006India
A. Ahmed
Affiliation:
Department of Mathematics & StatisticsUniversity of KashmirHazratbal, Srinagar-190 006India
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Abstract

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Usual duality results are proved for Wolfe and Mond-Weir type multiobjective symmetric dual problems without nonnegativity constraints under invexity/generalised invexity assumptions. Moreover, assuming the kernel function to be skew symmetric, the multiobjective problems are exhibited to be self duals.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1997

References

[1]Borwein, J.M., Optimization with respect to partial ordering, D.Phil. Thesis (Oxford University, 1974).Google Scholar
[2]Chandra, S. and Husain, I., ‘Symmetric dual nondifferentiable programs’, Bull. Austral. Math. Soc. 24 (1981), 295307.CrossRefGoogle Scholar
[3]Craven, B.D., ‘Lagrangian conditions and quasiduality’, Bull. Austral. Math. Soc. 16 (1977), 325339.CrossRefGoogle Scholar
[4]Dantzig, G.B., Eisenberg, E. and Cottle, R.W., ‘Symmetric dual nonlinear programs’, Pacific J. Math 15 (1965), 809812.CrossRefGoogle Scholar
[5]Dorn, W.S., ‘A symmetric dual theorem for quadratic programs’, J. Oper. Res. Soc. Japan 2 (1960), 9397.Google Scholar
[6]Geoffrion, A.M., ‘Proper efficiency and the theory of vector maximization’, J. Math. Anal. Appl. 22 (1968), 618630.CrossRefGoogle Scholar
[7]Hanson, M.A., ‘On sufficiency of the Kuhn-Tucker conditions’, J. Math. Anal. Appl. 80 (1981), 545550.CrossRefGoogle Scholar
[8]Mond, B. and Cottle, R.W., ‘Self duality in mathematical programming’, SIAM J. Appl. Math. 14 (1966), 420423.CrossRefGoogle Scholar
[9]Mond, B. and Hanson, M.A., ‘Symmetric duality for variational problems’, J. Math. Anal. Appl. 23 (1968), 161172.CrossRefGoogle Scholar
[10]Mond, B. and Weir, T., ‘Generalized concavity and duality’, in Generalized concavity and duality in optimization and economics, (Schaible, S. and Ziemba, W.T., Editors) (Academic Press, New York, 1981), pp. 263279.Google Scholar
[11]Smart, I. and Mond, B., ‘Symmetric duality with invexity in variational problems’, J. Math. Anal. Appl. 152 (1992), 536545.CrossRefGoogle Scholar
[12]Weir, T. and Mond, B., ‘Symmetric and self duality in multiple objective programming’, Asia-Pacific J. Oper. Res. 5 (1988), 124133.Google Scholar