Abstract
In this paper, we study different vector-valued Lagrangian functions and we develop a duality theory based upon these functions for nonlinear multiobjective programming problems. The saddle-point theorem and the duality theorem are derived for these problems under appropriate convexity assumptions. We also give some relationships between multiobjective optimizations and scalarized problems. A duality theory obtained by using the concept of vector-valued conjugate functions is discussed.
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Tanino, T., andSawaragi, Y.,Duality Theory in Multiobjective Programming, Journal of Optimization Theory and Applications, Vol. 27, pp. 509–529, 1979.
Tanino, T., andSawaragi, Y.,Conjugate Maps and Duality in Multiobjective Optimization, Journal of Optimization Theory and Applications, Vol. 31, pp. 473–479, 1980.
Bitran, G. R.,Duality for Nonlinear Multiple-Criteria Optimization Problems, Journal of Optimization Theory and Applications, Vol. 35, pp. 367–401, 1981.
Corley, H. W.,Duality Theory for Maximizations with Respect to Cones, Journal of Mathematical Analysis and Applications, Vol. 84, pp. 560–568, 1981.
Rockafellar, T. R.,Convex Analysis, Princeton University Press, Princeton, New Jersey, 1970.
Luenberger, D. G.,Optimization by Vector Space Methods, Wiley, New York, New York, 1969.
Luc, D. T.,M-Optimality and Dynamic Programming (to appear).
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Communicated by G. Leitmann
The author is grateful to the reviewer for many valuable comments and helpful suggestions.
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Luc, D.T. On duality theory in multiobjective programming. J Optim Theory Appl 43, 557–582 (1984). https://doi.org/10.1007/BF00935006
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DOI: https://doi.org/10.1007/BF00935006