Abstract
The aim of this paper is to establish some second order necessary and sufficient optimality conditions for a multiobjective problem where optimality is studied with respect to arbitrary closed convex cones. The proposed approach is an extension to the one recently given by the same authors.
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References
M.S. Bazaraa and C.M. Shetty, Foundations of optimization, Lecture Notes in Economics and Mathematical Systems 122, Springer-Verlag, 1976.
A. Ben-Tal, Second-order and related extremelity conditions in nonlinear programming, Journal of Opt. Theory and Applications 31, n°2 (1980) 143–165.
A. Ben-Tal and J. Zowe, A unified theory of first and second order conditions for extremum problems in topological vector spaces, Mathematical Programming Study 19 (1982) 39–76.
J.M. Borwein, Proper efficient points for maximizations with respect to cones, SIAM Journal Control Opt. 15 (1977) 57–63.
A. Cambini and L. Martein, Some optimality conditions in vector optimization, Journal of Informations and Opt. Sciences 10, n°1 (1989) 141–151.
A. Cambini and L. Martein, Tangent cones in optimization, in “Generalized Concavity for Economic Applications, Proceedings of the Workshop held in Pisa, April 2, 1992”, edited by P. Mazzoleni, Tecnoprint, Bologna (1992) 29–39.
A. Cambini and L. Martein, in “Generalized Convexity”, edited by S. Komlósi, T. Rapcsâk, and S. Schaible, Springer-Verlag (1994) 337–357.
A. Cambini and L. Martein, A survey of recent results in vector optimization, in “Optimization of Generalized Convex Problems”, edited by P. Mazzoleni (1994) 39–55.
A. Cambini and L. Martein, Second order necessary optimality conditions in the image space: preliminary results, in “Scalar and Vector Optimization in Economic and Financial Problems, Proceedings of the Workshop held in Milan, March 28, 1995”, edited by E. Castagnoli and G. Giorgi, (1995) 27–38.
R. Cambini, Second order optimality conditions in the image space, Report n. 99, Dept. Statistics and Applied Mathematics, University of Pisa, 1996.
R. Cambini, Generalized Concavity and Optimality Conditions in Vector Optimization, in “Operations Research and its Applications”, Proceedings of ISORA`96, World Publishing Corporation, Beijing (1996) pp. 172–180.
L. Martein, Some results on regularity in vector optimization, Optimization 20 (1989) 787–798.
L. Martein, Stationary points and necessary conditions in vector extremum problems, Journal of Informations and Optimiz. Sciences 10, n°1 (1989) 105–128.
L. Martein, Soluzioni efficienti e condizioni di ottimalità nell’ottimizzazione vettoriale, in “Metodi di Ottimizzazione per le Decisioni”, Masson, Milano (1994) 215–241.
G.P. McCormick, Second order conditions for constrained minima, SIAM Journal of Applied Mathematics 15, n°3 (1967) 641–652.
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© 1997 Springer-Verlag Berlin Heidelberg
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Cambini, A., Martein, L., Cambini, R. (1997). A New Approach to Second Order Optimality Conditions in Vector Optimization. In: Caballero, R., Ruiz, F., Steuer, R. (eds) Advances in Multiple Objective and Goal Programming. Lecture Notes in Economics and Mathematical Systems, vol 455. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46854-4_24
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DOI: https://doi.org/10.1007/978-3-642-46854-4_24
Publisher Name: Springer, Berlin, Heidelberg
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