Abstract
This paper deals with semi-infinite convex optimization problems. In particular, a regularity condition introduced recently by Guerra and Jimenez for the lin ear case is extended to the convex case, employing a suitable generalization of Haar’s condition. The convergence of an exchange process under such Haar-like conditions is investigated.
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A. Ben-Tal, E. Rosinger and A. Ben-Israel. A Helly-Type Theorem and Semi-infinite Programming. In: C.V. Coffman and G.J. Fix, editors, Con structive Approches to Mathematical Models, pages 127–135, Academic Press, 1979.
E. Blum, W. Oettli. Mathematische Optimierung, Springer-Verlag, 1975.
F. H. Clarke, Yu. S. Ledyaev and R. J. Stern. Complements, approximations, smoothings and invariance properties, Journal of Convex Analysis, 4:189–219, 1997.
H. G. Eggleston. Convexity, Cambridge University Press, Cambridge, 1969.
K. Fan, I. Glicksberg and A. J. Hoffman. Systems of inequalities involv ing convex functions, Proceedings of the American Mathematical Society, 8:617–622, 1957.
W. Fenchel. über konvexe Funktionen mit vorgeschriebenen Niveauman nigfaltigkeiten, Mathematische Zeitschrift, 63:496–506, 1956.
F. Giannessi. General optimality conditions via a separation scheme. In E. Spedicato, editor, Algorithms for Continuous Optimization, Kluwer, pages 1–23, 1994.
F. Guerra and M. A. Jimenez. On feasible sets defined through Chebyshev approximation, Mathematical Metfiods of Operations Research, 47:255–264, 1998.
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© 2001 Springer Science+Business Media Dordrecht
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Hassouni, A., Oettli, W. (2001). On Regularity and Optimality in Nonlinear Semi-Infinite Programming. In: Goberna, M.Á., López, M.A. (eds) Semi-Infinite Programming. Nonconvex Optimization and Its Applications, vol 57. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3403-4_3
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DOI: https://doi.org/10.1007/978-1-4757-3403-4_3
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-5204-2
Online ISBN: 978-1-4757-3403-4
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