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C^1'1 vector optimization problems and Riemann derivatives

Ginchev I., Guerraggio A., Rocca M.

Control and Cybernetics

2004

Vol. 33, no 2

259-273

In this paper we introduce a generalized second-order Riemann-type derivative for C^1'1 vector functions and use it to establish necessary and sufficient optimality conditions for vector optimization problems. We show that, these conditions are stronger than those obtained by means of the second-order subdinerential in Clarke sense considered in Guerraggio, Luc (2001) and also to some extent than those obtained in Guerraggio, Luc, Minh (2001).

Second-order characterizations of convex and pseudoconvex functions

Ginchev I., Ivanov V. I.

Journal of Applied Analysis

2003

Vol. 9, nr 2

261-273

The present paper gives characterizations of radially u.s.c. convex and pseudoconvex functions f: X —> R defined on a convex subset X of a real linear space E in terms of first and second-order upper Dini-directional derivatives. Observing that the property f radially u.s.c. does not require a topological structure of E, we draw the possibility to state our results for arbitrary real linear spaces. For convex functions we extend a theorem of Huang, Ng [10]. For pseudoconvex functions we generalize results of Diewert, Avriel, Zang [6] and Crouzeix [4]. While some known results on pseudoconvex functions are stated in global concepts (e.g. Komlosi [11]), we succeeded in realizing the task to confine to local concepts only.