Moreau’s Proximal Mappings and Convexity in Hamilt

Authors: R Tyrrell Rockafellar

Publish Date: 2006

Volume: , Issue: , Pages: 3-12

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Abstract

Proximal mappings which generalize projection mappings were introduced by Moreau and shown to be valuable in understanding the subgradient properties of convex functions Proximal mappings subsequently turned out to be important also in numerical methods of optimization and the solution of nonlinear partial differential equations and variational inequalities Here it is shown that when a convex function is propagated through time by a generalized HamiltonJacobi partial differential equation with a Hamiltonian that is concave in the state and convex in the costate the associated proximal mapping exhibits locally Lipschitz dependence on time Furthermore the subgradient mapping associated of the value function associated with this mapping is graphically Lipschitzian

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