Abstract
Necessary conditions of Fritz John and Kuhn-Tucker type for Pareto optimality are derived by first reducing a vector minimization problem (multiobjective programming) to a system of scalar minimization problems and then using known results in convex programming.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Arrow, K. J., Hurwicz, L., andUzawa, H.,Studies in Linear and Nonlinear Programming, Stanford University Press, Stanford, California, 1958.
Dacunha, N. O., andPolak, E.,Constrained Minimization under Vector-Valued Criteria in Finite-Dimensional Spaces, Journal of Mathematical Analysis and Applications, Vol. 10, pp. 103–124, 1967.
Kuhn, H. W., andTucker, A. W.,Nonlinear Programming, Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, Berkeley, California, pp. 416–427, 1950.
Tanino, T., andSawaraki, Y.,Duality Theory in Multiobjective Programming, Journal of Optimization Theory and Applications, Vol. 27, pp. 509–529, 1979.
Schechter, M.,More on Subgradient Duality, Journal of Mathematical Analysis and Applications, Vol. 71, pp. 251–262, 1979.
Rockafellar, R. T.,Convex Analysis, Princeton University Press, Princeton, New Jersey, 1970.
Author information
Authors and Affiliations
Additional information
Communicated by G. Leitmann
This research was supported by the University Grants Commission of India. The author wishes to thank Dr. Sundaram M. A. Sastry for his helpful suggestions and useful comments.
Rights and permissions
About this article
Cite this article
Kanniappan, P. Necessary conditions for optimality of nondifferentiable convex multiobjective programming. J Optim Theory Appl 40, 167–174 (1983). https://doi.org/10.1007/BF00933935
Issue Date:
DOI: https://doi.org/10.1007/BF00933935