Abstract
For a vector extremum problem, optimality conditions, regularity and duality can be studied by means of vector-valued weak separation functions; in this paper duality theorems are established for a wide class of multiobjective problems, by choosing a suitable class of vector-valued weak separation functions which is strictly related to a generalized vector-valued Lagrangian function. The suggested approach allows us to obtain some regulatiry conditions.
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References
Bit ran G.R., Duality for Nonlinear Multiple-Criteria Optimization Problems. J.O.T.A., vol. 35, (1981), pp.367–401.
Bitran G.R., Magnanti T.L., The Structure of Admissible Points with Respect to Cone Dominance. J.O.T.A.. vol. 29 (1979), pp. 583–614.
Cambini A., Nonlinear Separation Theorems. Duality and Optimality Conditions, in: Optimization and Related Fields, Lecture Notes in Math., n° 1190, Springer Verlag (1986).
Cambini A., Martein L., Separation Functions and Optimality Conditions in Vpctor Extremum Problems. University of Pisa, Dep. of Mathematics, Optimization and Operations Reserach Section, Paper A-120, (1984).
Cambini A., Martein L., Some Optimality Conditions in Vector Optimization. Journal of Information and Optimization Sciences, vol. 10, n° 1, (1989).
Giannessi F., Theorems of the Alternative and Optimality Conditions. J.O.T.A., vol. 42, (1984) pp. 331–365.
Jahn J., Duality in Vector Optimization. Mathematical Programming, vol. 25 (1983), pp. 343–353.
T. Luc D., On Duality Theory in Multiobjective Programming. J.O.T.A., vol. 43 (1984) PP. 557–582.
Martein L., Sulla Dualità Lagraneiana Esponenziale. University of Pisa, Dep. of Mathematics, Optimization and Operations Research Section, paper A-l 14 (1984).
Martein L., Regularity Conditions for Constrained Extremum Problems. J.O.T.A., vol. 47,(1985), pp. 217–233.
Martein L., Stationary Points and Necessary Conditions in Vector Extremum Problems. Journal of information and Optimization Sciences, vol. 10, n° 1, (1989).
Martein L., Lagrange Multipliers and Generalized Differentiate Functions in Vector Extremum Problems, to appear in journal of Optimization Theory and Applications.
Martein L., Some Results on Regularity in Vector Optimization, vol. 20, n° 6, (1989), pp. 787–798.
Nakayama H., Duality Theory in Vector Optimization: an overview. Research Report, Dep. of Applied Mathematics, Konon University (1979).
Tanino T., Sawaragi Y., Duality Theory in Multiobjective Programming. J.O.T.A., vol. 27, (1979) pp. 509–529.
Sawaragi Y., Nakayama H., Tanino T., Theory of Multiobjective Optimization. Academic Press, Inc. (1985).
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Martein, L. (1990). An Approach to Lagrangian Duality in Vector Optimization. In: Cambini, A., Castagnoli, E., Martein, L., Mazzoleni, P., Schaible, S. (eds) Generalized Convexity and Fractional Programming with Economic Applications. Lecture Notes in Economics and Mathematical Systems, vol 345. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46709-7_17
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DOI: https://doi.org/10.1007/978-3-642-46709-7_17
Publisher Name: Springer, Berlin, Heidelberg
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