Journal of Convex Analysis 13 (2006), No. 3, 647--685
Copyright Heldermann Verlag 2006
On the Variational Behaviour of the Subhessians of the Lasry-Lions Envelope
Andrew Eberhard
Mathematics Department, RMIT -- GPO Box 2476V, Melbourne, Vict. 3001, Australia
andrew.eberhard@ems.rmit.edu.au
Rajalingam Sivakumaran
Mathematics Department, RMIT -- GPO Box 2476V, Melbourne, Vict. 3001, Australia
siva.rajalingam@rmit.edu.au
Robert Wenczel
Mathematics Department, RMIT -- GPO Box 2476V, Melbourne, Vict. 3001, Australia
e01928@ems.rmit.edu.au
A full analysis is made of the effect that the Lasry-Lions double-envelope has on the subjet and associated subhessians of a prox-bounded, lower-semicontinuous function. This enables the (basic) subdifferential of nonsmooth analysis and the limiting subjet of viscosity-solution theory to be characterized via accumulation points of the first- and second-order derivative information of approximating functions provided by the Lasry-Lions double-envelope.
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