Abstract: Proximal mappings, introduced by J.-J. Moreau in the 1960's as generalizations of orthogonal projections, are useful in analyzing the subgradient properties of convex functions. They are also found important in numerical
methods of optimization and the solution of partial di®erential equations and variational inequalities, and in the Hamilton-Jacobi theory of convex functions as well. Moreover, it was recently realized that proximal mappings are helpful in image modeling since they can be used to e®ectively minimize the sum of two convex functions.
In this talk, I will ¯rst present basic properties of Moreau's proximal calculus and the Moreau decomposition, and then discuss the proximity algorithm for minimizing the sum of two convex functions. Applications to image denoising will be also discussed.
Tea Time: 3:30pm R707