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Journal of Convex Analysis 18 (2011), No. 1, 181--202
Copyright Heldermann Verlag 2011

Second-Order Asymptotic Directions of Unbounded Sets with Application to Optimization

Nicolas Hadjisavvas
Dept. of Product and Systems Design, University of the Aegean, 84100 Hermoupolis - Syros, Greece

Dinh The Luc
Laboratoire ANLG EA 2151, University of Avignon, 33 Rue Louis Pasteur, 84000 Avignon, France

We introduce a new concept of second-order asymptotic directions of unbounded sets and apply it to establish global optimality conditions of nonlinear functions on unbounded sets, existence conditions for efficient points in a partially ordered space, and to extend Dieudonné's theorem on the closedness of the sum of two closed sets.

Keywords: First-order and second-order asymptotic directions; optimality conditions; efficient points.

MSC: 90C30, 90C29, 49J52

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