Practical Aspects of the Moreau-Yosida Regularization: Theoretical Preliminaries

By Claude Lemaréchal, Claudia A. Sagastizábal. 1997

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Citations in the corpus

Bregmanized Nonlocal Regularization for Deconvolution and Sparse Reconstruction (2010, methodology): “If we apply an inexact Uzawa method [47] and Moreau-Yosida proximal point iteration [32] on this formulation, we get the following algorithm: { step 1: u = minu ( μJ(u) + 12 ||Au− f ||2 − 〈Au− f, p − f〉+ ||u− u||(2)D ) step 2: p = p − (Au − f) (18) where D is a positive-definite matrix.”
Randomized Smoothing for Stochastic Optimization (2011, methodology): “Such approaches for deterministic non-smooth problems are by now well-known, and include Moreau-Yosida regularization (e.g. [22]), methods based on recession functions [3]; and a method that uses conjugate and proximal functions [26].”
More efficiency in multiple kernel learning (2007, background): “The more the kernel matrices, J(·)is convex, di.erentiable with Lipschitz gradient (Lemar´echal & Sagastizabal, 1997).”
Implicit Deep Learning (2019, unknown): “˚(P;AX+ BU) + 2 kX Pk2 F + P(A;B;C;D); (10) with >0 an additional parameter. This approach is closely related to the Moreau-Yosida regularization of the divergence function f ˚, which is smooth [14]. The above model involves a single “dual” variable associated with the activation constraint. It ”
Multiple kernel learning, conic duality, and the SMO algorithm (2004, methodology): “In particular, Moreau-Yosida (MY) regularization is an eﬀec-tive general solution methodology that is based on inf-convolution (Lemarechal & Sagastizabal, 1997).”
Forward–backward quasi-Newton methods for nonsmooth optimization problems (2016, unknown): “n argmin’= zerr’ for all 2(0;1=Lf). 2.3. Second-order properties. The FBE is not everywhere twice continuously dierentiable in general. For example, if gis real valued then g 2C2 if and only if g2C2 [34]. However, second order properties will only be needed at critical points of ’in our framework, a”
Proximal Algorithms (2013, background): “The idea of the Moreau envelope (sometimes called MoreauYosida regularization) traces back to Moreau and to Yosida’s work in functional analysis [200]; see [122, 123] for some more recent work.”