Under differentiability assumptions, Fritz John Sufficient optimality conditions are proved for a nonlinear programming problem in which the objective function is assumed to be quasiconvex and the constraint functions are assumed to quasiconcave/strictly pseudoconcave. Duality theorems are proved for Mond-Weir type duality under the above generalized convexity assumptions.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
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.
Mangasarian, O. L.,Nonlinear Programming, McGraw-Hill, New York, New York, 1969.
Bhatt, S. K., andMisra, S. K.,Sufficient Optimality Criteria in Nonlinear Programming in the Presence of Convex Equality and Inequality Constraints, Zeitschrift für Operations Research, Series A, Vol. 19, pp. 101–105, 1975.
Bector, C. R., andGrover, T. R.,On a Sufficient Optimality Theorem of Mangasarian in Nonlinear Programming, Cahiers du Centre d'Etudes de Recherche Operationnelle, Vol. 16, pp. 12–14, 1974.
Bector, C. R., andGulati, T. R.,Sufficient Optimality Conditions in Presence of Quasi-Convex Equality Constraints, Mathematische Operationsforschung und Statistik, Series Optimization, Vol. 8, pp. 181–184, 1977.
Singh, C.,Sufficient Optimality Criteria in Nonlinear Programming for Generalized Equality-Inequality Constraints, Journal of Optimization Theory and Applications, Vol. 22, pp. 631–635, 1977.
Skarpness, B., andSposito, V. A.,A Modified Fritz John Optimality Criterion, Journal of Optimization Theory and Applications, Vol. 31, pp. 113–115, 1980.
Bector, C. R., andBector, M. K.,On Various Duality Theorems in Nonlinear Programming, Journal of Optimization Theory and Applications, Vol. 53, pp. 509–515, 1987.
Ponstein, J.,Seven Kinds of Convexity, SIAM Review, Vol. 9, pp. 115–119, 1967.
Mangasarian, O. L., andFromovitz, S.,The Fritz John Necessary Optimality Conditions in the Presence of Equality and Inequality Constraints, Journal of Mathematical Analysis and Applications, Vol. 17, pp. 37–47, 1967.
Bector, C. R., Bector, M. K., andKlassen, J. E.,Duality for a Nonlinear Programming Problem, Utilitas Mathematica, Vol. 11, pp. 87–99, 1977.
Craven, B. D.,Invex Functions and Constrained Local Minima, Bulletin of the Australian Mathematical Society, Vol. 24, pp. 357–366, 1981.
The first author is thankful to the Natural Science and Engineering Research Council of Canada for financial support through Grant No. A-5319. The authors are thankful to Professor B. Mond for suggestions that improved the original draft of the paper.
Communicated by G. Leitmann
About this article
Cite this article
Bector, C.R., Chandra, S. & Bector, M.K. Sufficient optimality conditions and duality for a quasiconvex programming problem. J Optim Theory Appl 59, 209–221 (1988). https://doi.org/10.1007/BF00938309
- Fritz John sufficient optimality conditions
- Mond-Weir duality