Abstract
Recently, Gulati and Craven and Mond and Egudo established strict converse duality theorems for some of Mond-Weir duals for nonlinear programming problems. Here, we establish various duality theorems under weaker convexity conditions that are different from those of Gulati and Craven, Mond and Weir, and Mond and Egudo.
Similar content being viewed by others
References
Mond, B., andWeir, T.,Generalized Concavity and Duality, Generalized Concavity in Optimization and Economics, Edited by S. Schaible and W. T. Ziemba, Academic Press, New York, New York, pp. 263–280, 1981.
Wolfe, P.,A Duality Theorem for Nonlinear Programming, Quarterly of Applied Mathematics, Vol. 19, pp. 239–244, 1961.
Gulati, T. R., andCraven, B. D.,A Strict Converse Duality Theorem in Nonlinear Programming, Journal of Information and Optimization Sciences, Vol. 4, pp. 301–306, 1983.
Mangasarian, O. L.,Nonlinear Programming, McGraw-Hill, New York, New York, 1969.
Mond, B., andEgudo, R. R.,On Strict Converse Duality in Nonlinear Programming, Journal of Information and Optimization Sciences, Vol. 6, pp. 113–116, 1985.
Ponstein, J.,Seven Kinds of Convexity, SIAM Review, Vol. 9, pp. 115–119, 1967.
Bector, C. R., Chandra, S., andHussain, I.,Generalized Concavity and Duality in Continuous Programming, Utilitas Mathematica, Vol. 25, pp. 171–190, 1984.
Bector, C. R., andBhatt, S. K.,Nonlinear Programming in Complex Space: Necessary and Sufficient Conditions, Revue Roumaine de Mathématiques Pures at Appliquées, Vol. 30, pp. 497–503, 1985.
Bector, C. R., andBhatia, B. L.,Generalized Duality for Nonlinear Programming on Complex Space, Economic Computation and Economic Cybernetics Studies and Research, Vol. 2, pp. 75–80, 1985.
Craven, B. D.,Invex Functions and Constrained Local Minima, Bulletin of Australian Mathematical Society, Vol. 24, pp. 357–366, 1981.
Hanson, M. A.,On Sufficiency of the Kuhn-Tucker Conditions, Journal of Mathematical Analysis and Applications, Vol. 80, pp. 545–550, 1980.
Mahajan, D. G., andVartak, M. N.,Generalization of Some Duality Theorems in Nonlinear Programming, Mathematical Programming, Vol. 12, pp. 293–317, 1977.
Rockafellar, R. T.,Convex Analysis, Princeton University Press, Princeton, New Jersey, 1970.
Bector, C. R., Bector, M. K., andKlassen, J. E.,Duality for a Nonlinear Programming Problem, Utilitas Mathematica, Vol. 11, pp. 87–99, 1977.
Author information
Authors and Affiliations
Additional information
Communicated by G. Leitmann
The first author is thankful to the Natural Science and Engineering Research Council of Canada for financial support through Grant A-5319.
Rights and permissions
About this article
Cite this article
Bector, C.R., Bector, M.K. On various duality theorems in nonlinear programming. J Optim Theory Appl 53, 509–515 (1987). https://doi.org/10.1007/BF00938952
Issue Date:
DOI: https://doi.org/10.1007/BF00938952