Abstract
Necessary and sufficient conditions of Fritz John type for Pareto optimality of multiobjective programming problems are derived. This article suggests to establish a Wolfe-type duality theorem for nonlinear, nondifferentiable, convex multiobjective minimization problems. The vector Lagrangian and the generalized saddle point for Pareto optimality are studied. Some previously known results are shown to be special cases of the results described in this paper.
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References
Kanniappan, P.,Necessary Conditions for Optimality of Nondifferentiable Convex Multiobjective Programming, Journal of Optimization Theory and Applications, Vol. 40, pp. 167–174, 1983.
Kanniappan, P., andSastry, S. M. A.,Duality Theorems and an Optimality Condition for Nondifferentiable Convex Programming, Journal of the Australian Mathematical Society, Series A, Vol. 32, pp. 369–379, 1982.
Lai, H. C., andLiu, J. C.,Necessary and Sufficient Conditions for Pareto Optimality in Nondifferentiable Convex Multiobjective Programming, National Tsing Hua University, Taiwan, Preprint, 1984.
Tanino, T., andSawaragi, Y.,Duality Theory in Multiobjective Programming, Journal of Optimization Theory and Applications, Vol. 27, pp. 509–529, 1979.
Wolfe, P.,A Duality Theorem for Nonlinear Programming, Quarterly of Applied Mathematics, Vol. 19, pp. 239–244, 1961.
Schechter, M.,A Subgradient Duality Theorem, Journal of Mathematical Analysis and Applications, Vol. 61, pp. 850–855, 1977.
Schechter, M.,More on Subgradient Duality, Journal of Mathematical Analysis and Applications, Vol. 71, pp. 251–262, 1979.
Mond, B., andZlobec, S.,Duality for Nondifferentiable Programming with a Constraint Qualification, Utilitas Mathematica, Vol. 15, pp. 291–302, 1979.
Censor, Y.,Pareto Optimality in Multiobjective Problems, Applied Mathematics and Optimization, Vol. 4, pp. 41–59, 1979.
Minami, M.,Weak Pareto Optimality of Multiobjective Problems in a Locally Convex Linear Topological Space, Journal of Optimization Theory and Applications, Vol. 34, pp. 469–484, 1981.
Nieuwenhuis, J. W.,Some Minimax Theorems in Vector-Valued Functions, Journal of Optimization Theory and Applications, Vol. 40, pp. 463–475, 1983.
Jahn, J.,Duality in Vector Optimization, Mathematical Programming, Vol. 25, pp. 343–353, 1983.
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Communicated by P. L. Yu
This research was partly supported by the National Science Council, Taipei, ROC.
The authors would like to thank the two referees for their valuable suggestions on the original draft.
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Lai, H.C., Ho, C.P. Duality theorem of nondifferentiable convex multiobjective programming. J Optim Theory Appl 50, 407–420 (1986). https://doi.org/10.1007/BF00938628
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DOI: https://doi.org/10.1007/BF00938628