Smoothing and First Order Methods: A Unified Framework

By Amir Beck, Marc Teboulle. 2012

336 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mathematical Physics, Numerical Analysis

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Citations in the corpus

A simple algorithm for a class of nonsmooth convex-concave saddle-point problems (2015, background): “Another approach is to exploit the “max-structure” inherently present in an SP formulation and combine smoothing with fast gradient schemes [15, 3].”
A Superquantile Approach to Federated Learning with Heterogeneous Devices (2021, background): “This yields that G θ is Algorithm 1 Alternating Minimization for ∆ - FL where h ν ( ρ ) = min u max { u, 0 } + ( u − ρ ) 2 / (2 ν ) is the so-called Moreau envelope of max {· , 0 } , It provides a smooth and tractable uniform approximation [13].”
Optimal Black-Box Reductions Between Optimization Objectives (2016, background): “Beck and Teboulle [5] give a reduction from Case 4 to Case 2.”
Proximal Algorithms (2013, result): “This perspective is very related to recent work by Nesterov [150]; for more on this connection, see [19].”
C-MIL: Continuation Multiple Instance Learning for Weakly Supervised Object Detection (2019, methodology): “Smoothing is an important technique in optimization [4] and has been applied in deep neural networks.”
On the Convergence of Alternating Minimization for Convex Programming with Applications to Iteratively Reweighted Least Squares and Decomposition Schemes (2015, neutral): “, [3]), r(w) − Lr ρ ≤ rρ(w) ≤ r(w) for all w ∈ R,”
Loss Functions for Top-k Error: Analysis and Insights (2015, methodology): “Our new family of smooth top-k hinge losses is based on the Moreau-Yosida regularization [4, 26].”
Weiszfeld’s Method: Old and New Results (2014, background): “, [36,41]), but we have chosen to provide a self-contained proof.”
Learning Classifiers with Fenchel-Young Losses: Generalized Entropies, Margins, and Algorithms (2018, methodology): “Fenchel duality also plays a key role in smoothing techniques (Nesterov, 2005; Beck and Teboulle, 2012), which have been used extensively to create smoothed losses (Shalev-Shwartz and Zhang, 2016).”