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Duality in nonconvex vector minimum problems

Published online by Cambridge University Press:  17 April 2009

T.R. Gulati
Affiliation:
Department of Mathematics, University of Roorkee, Roorkee, India247667
Nadia Talaat
Affiliation:
Department of Mathematics, University of Alexandria, Egypt
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Abstract

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A nonlinear vector minimum problem is considered. Duality theorems are proved for Mond-Weir type dual and their application to a certain nonlinear fractional vector minimum problem is discussed.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1991

References

[1]Bector, C.R., Chandra, S. and Durgaprasad, M.V., ‘Duality in pseudolinear multiobjective programming’, Asia-Pacific J. Oper. Res. 5 (1988), 150159.Google Scholar
[2]Craven, B.D., ‘Lagrangian conditions and quasiduality’, Bull. Austral. Math. Soc. 16 (1977), 325339.CrossRefGoogle Scholar
[3]Geoffrion, A.M., ‘Proper efficiency and the theory of vector maximization’, J. Math. Anal. Appl. 22 (1968), 618630.Google Scholar
[4]Mangasarian, O.L., Nonlinear programming (McGraw-Hill, New York, 1969).Google Scholar
[5]Mond, B. and Weir, T., ‘Generalized concavity and duality’, in Generalized concavity in optimization and economics, Editors Schaible, S. and Ziemba, W.T., pp. 263279 (Academic Press, New York, 1981).Google Scholar
[6]Singh, C., ‘Optimality conditions in multiobjective differentiable programming’, J. Optim. Theory Appl 53 (1987), 115123.CrossRefGoogle Scholar
[7]Singh, C., ‘Duality theory in multiobjective differentiable programming’, J. Inform. Optim. Sci. 9 (1988), No. 2, 231240.Google Scholar
[8]Weir, T., ‘Proper efficiency and duality for vector valued optimization problems’, J. Austral. Math. Soc., Series A 43 (1987), 2134.CrossRefGoogle Scholar
[9]Weir, T. and Jeyakumar, V., ‘A class of nonconvex functions and mathematical programming’, Bull. Austral. Math. Soc. 38 (1988), 177189.CrossRefGoogle Scholar
[10]Weir, T. and Mond, B., ‘Generalized convexity and duality in multiple objective programming’, Bull. Austral. Math. Soc. 39 (1989), 287299.CrossRefGoogle Scholar