Mathematics – Optimization and Control
Scientific paper
2011-06-12
Mathematics
Optimization and Control
24 pages, 3 figures
Scientific paper
For a set-valued map, we characterize, in terms of its (unconvexified or convexified) graphical derivatives near the point of interest, positively homogeneous maps that are generalized derivatives in the sense of [17]. This result generalizes the Aubin criterion in [8]. A second characterization of these generalized derivatives is easier to check in practice, especially in the finite dimensional case. Finally, the third characterization in terms of limiting normal cones and coderivatives generalizes the Mordukhovich criterion in the finite dimensional case. The convexified coderivative has a bijective relationship with the set of possible generalized derivatives. We conclude by using the above results to describe the generalized differentiability properties of constraint systems, which includes the case of mixed equalities and inequalities satisfying the Mangasarian-Fromovitz constraint qualification as a particular example.
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