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Optimality and duality in continuous-time nonlinear fractional programming

Published online by Cambridge University Press:  17 February 2009

S. Suneja ,
C. Singh  and
R. N. Kaul
S. Suneja
Affiliation:
Department of Mathematics, Miranda House, University of Delhi, Delhi—110007, India.
C. Singh
Affiliation:
Department of Mathematics, St. Lawrence University, Canton, NY 13617, USA.
R. N. Kaul
Affiliation:
Department of Mathematics, University of Delhi, Delhi—1100007, India.
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Abstract

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Optimality conditions via subdifferentiability and generalised Charnes-Cooper transformation are obtained for a continuous-time nonlinear fractional programming problem. Perturbation functions play a key role in the development. A dual problem is presented and certain duality results are obtained.

Type
Research Article
Information
The ANZIAM Journal , Volume 34 , Issue 2 , October 1992 , pp. 229 - 244
Copyright
Copyright © Australian Mathematical Society 1992

References

[1]Bellman, R., “Bottleneck problems and dynamic programming”, Proc. Math. Acad. Sci. USA 39 (1953) 947–951.CrossRefGoogle ScholarPubMed
[2]Farr, W. H. and Hanson, M. A., “Continuous time programming with nonlinear constraints”, J. Math. Anal. Appl 45 (1974) 96–115.CrossRefGoogle Scholar
[3]Farr, W. H. and Hanson, M. A., “Continuous time programming with nonlinear time delayed constraints”, J. Math. Anal. Appl. 46 (1974) 41–61.CrossRefGoogle Scholar
[4]Geoffrion, A. M., “Duality in nonlinear programming: A simplified application-oriented development”, SIAM Review 13 (1971) 1–37.CrossRefGoogle Scholar
[5]Hanson, M. A. and Mond, B., “A class of continuous convex programming problems”, J. Math. Anal. Appl. 22 (1968) 427–437.CrossRefGoogle Scholar
[6]Kaul, R. N. and Kaur, S., “Sufficient optimality criteria in continuous time programming”, J. Math. Anal. Appl. 88 (1982) 37–47.CrossRefGoogle Scholar
[7]Levinson, N., “A class of continuous linear programming problems”, J. Math. Anal. Appl. 16 (1966) 73–83.CrossRefGoogle Scholar
[8]Craven, B. D. and Mond, B., “Duality for homogeneous fractional programming”, Cahiers du Centre d'Etudes de Recherche Operationnelle 18 (1976) 413–417.Google Scholar
[9]Craven, B. D. and Mond, B., “A note on duality in homogeneous fractional programming”, Naval Research Logistics Quarterly 26 (1979) 153–155.CrossRefGoogle Scholar
[10]Schaible, S., “Fractional programming I: Duality,” Management Science 22 (1976) 858–867.CrossRefGoogle Scholar
[11]Singh, C., ‘A sufficient optimality criterion in continuous time programming for generalized convex functions”, J. Math. Anal. Appl. 62 (1978) 506–511.CrossRefGoogle Scholar
[12]Singh, C., “A saddlepoint of continuous time programming having inequality and equality constraints”, J Math. Anal. Appl. 64 (1978) 354–359.CrossRefGoogle Scholar
[13]Singh, C. and Farr, W. H., “Saddlepoint optimality criteria of continuous time programming without differentiability”, J. Math. Anal. Appl. 59 (1977) 442–453.CrossRefGoogle Scholar
[14]Tyndall, W. F., “A duality theorem for a class of continuous linear programming problems”, SIAM J. Appl. Math 13 (1965) 644–666.CrossRefGoogle Scholar
[15]Zalmai, G. J., “Optimality conditions and Lagrangian duality in continuous time nonlinear programming”, J. Math. Anal. Appl. 109 426–452.CrossRefGoogle Scholar
[16]Zalmai, G. J., “A continuous time generalization of Gordan's Transposition Theorem”, J. Math. Anal. Appl. 110 (1985) 130–140.CrossRefGoogle Scholar
[17]Zalmai, G. J., “The Fritz-John and Kuhn Tucker Optimality conditions in continuous time nonlinear programming”, J Math. Anal. Appl. 110 (1985) 503–518.CrossRefGoogle Scholar
[18]Zalmai, G. J., “Sufficient optimality conditions in continuous time nonlinear programming”, J. Math. Anal. Appl. 111 (1985) 130–147.CrossRefGoogle Scholar
[19]Zalmai, G. J., “Optimality conditions and duality for a class of continuous-time generalized fractional programming problems”, J. Math. Anal. Appl. 153 (1990) 356–371.CrossRefGoogle Scholar