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Weak sharp minima in multiobjective optimization

Studniarski M.

Control and Cybernetics

2007

Vol. 36, no 4

925-937

We extend some necessary and sufficient conditions for strict local Pareto minima of order m obtained by Jiménez (2002) to the case of weak ψ-sharp local Pareto minima, i.e., to the case when the local solution is not necessarily unique.

Calculus of second-order subdifferentials in infinite dimensions

Morduhovic B.

Control and Cybernetics

2002

Vol. 31, no 3

557-573

We study two types of second-order subdifferentials of extended-real-valued functions on Banach spaces that are important for applications in variational analysis, especially to sensitivity issues and second-order optimality conditions. The main concern of the paper is to derive extended sum and chain rules for these subdifferentials in the case of Asplund and general Banach spaces, which provide the basis for further theory and applications.