Journal of Convex Analysis 14 (2007), No. 2, 413--432
Copyright Heldermann Verlag 2007
On Moreau-Yosida Approximation and on Stability of Second-Order Subdifferentials of Clarke's Type
Nina Ovcharova
Institute of Mathematics, Department of Aerospace Engineering, Universität der Bundeswehr, Werner-Heisenberg-Weg 39, 85577 Neubiberg/München, Germany
nina.ovcharova@unibw-muenchen.de
Joachim Gwinner
Institute of Mathematics, Department of Aerospace Engineering, Universität der Bundeswehr, Werner-Heisenberg-Weg 39, 85577 Neubiberg/München, Germany
joachim.gwinner@unibw-muenchen.de
For the Gateaux derivative of a C1,1 function defined on a reflexive Banach space with Kadec norm || . ||, we use Moreau-Yosida regularization to show that Clarke's subdifferential of second-order can be weak*-approximated from below. Moreover, in the convex case we can strengthen the inclusion to an equality in the limit.
In another approach for C1,1 functions, we establish a weak* stability result for second-order subdifferentials of Clarke's type. We apply the latter result to the continuous behaviour of the Lagrange multipliers in second-order necessary optimality conditions under epi-convergent perturbations and to stability of second-order subdifferentials of Clarke's type of integral functionals and also of the standard type of functionals in the calculus of variations.
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