First-order conditions for \(C^{0,1}\) constrained vector optimization. (English) Zbl 1148.90011

Ginchev, I.; Guerraggio, A.; Rocca, M.

Giannessi, Franco (ed.) et al., Variational analysis and applications. Proceedings of the 38th conference of the School of Mathematics “G. Stampacchia” in memory of G. Stampacchia and J.-L. Lions, Erice, Italy, June 20–July 1, 2003. New York, NY: Springer (ISBN 0-387-24209-0/hbk; 0-387-24276-7/e-book ). Nonconvex Optimization and its Applications 79, 427-450 (2005).

The paper provides necessary and sufficient optimality conditions for Lipschitz vector optimization problems. The main results are Lemma 3 and Theorem 1. The authors use a scalarization technique to point out necessary optimality conditions for weak efficiency in terms of the Dini derivative. They establish also sufficient optimality conditions for a point to be an isolated minimizer of first order.
For the entire collection see [Zbl 1077.49001].

Reviewer: Nazih Abderrazzak Gadhi (Marrakech)

MSC:

90C29	Multi-objective and goal programming
90C46	Optimality conditions and duality in mathematical programming