joint work with Minh N. Dao, Regina S. Burachik
Recently, Burachik and Martinez-Legaz introduced a distance constructed from a representative function for a maximally monotone operator. This distance generalizes the Bregman distance, and we name it the Fitzpatrick distance. We explore the properties of its variants.
joint work with Panagiotis Patrinos
We provide a novel unified interpretation of nonconvex splitting algorithms as compositions of Lipschitz and set-valued majorization-minimization mappings. A convergence analysis is established based on proximal envelopes, a generalization of the Moreau envelope. This framework also enables the integration with fast local methods applied to the nonlinear inclusion encoding optimality conditions. Possibly under assumptions to compensate the lack of convexity, this setting is general enough to cover ADMM as well as forward-backward, Douglas-Rachford and Davis-Yin splittings.
joint work with Michael Friedlander, Ives Macedo
Polar envelope is a convolution operation specialized to gauges, and is analogous to Moreau envelope. In this talk, we discuss important properties of polar envelope and the corresponding polar proximal map. These include smoothness of the envelope function, and uniqueness and continuity of the proximal map. We also highlight the important roles the polar envelope plays in gauge duality and the construction of algorithms for gauge optimization.