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

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].

MSC:

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