A primal–dual fixed point algorithm for convex separable minimization with applications to image restoration

By Peijun Chen, Jianguo Huang, Xiaoqun Zhang. 2013

244 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Mathematical Physics

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Citations in the corpus

Distributed Fixed Point Methods with Compressed Iterates (2019, neutral): “The PAPC algorithm [10,17,32] is an algorithm for minimizing F + H ◦ L , where F is smooth and convex, H is nonsmooth and convex and L is a linear operator.”
Distributed Proximal Splitting Algorithms with Rates and Acceleration (2020, methodology): “IfR = 0, the PD3O and PDDY algorithms revert to the Loris–Verhoeven algorithm [17], also discovered independently as the PDFP2O [6] and PAPC [13] algorithms; see also [9, 10] for an analysis as a primal-dual forward-backward algorithm.”
A New Primal–Dual Algorithm for Minimizing the Sum of Three Functions with a Linear Operator (2016, methodology): “In [7], the PAPC iteration is shown to be nonexpansive only under a norm for X ×S that is deﬁned by z (cid:107) 2 + s (cid:107) 2 .”
Proximal Splitting Algorithms: A Tour of Recent Advances, with New Twists. (2020, methodology): “…𝑃 must be strongly positive, which is the case if and only if The following result makes it possible to have 2 = 1; it is a consequence of the analysis by O’Connor and Vandenberghe [48] of the PD3O algorithm [53], discussed in Section 7, of which the Loris–Verhoeven algorithm is a particular case.”
Dualize, Split, Randomize: Fast Nonsmooth Optimization Algorithms (2020, methodology): “In the deterministic case gk+1 = ∇F (xk), LiCoSGD reverts to an instance of the algorithm first proposed by Loris and Verhoeven in [52], and rediscovered independently as the PDFP2O algorithm [15] and the Proximal Alternating Predictor-Corrector (PAPC) algorithm [30].”
Proximal Algorithms in Statistics and Machine Learning (2015, background): “The differences often involve assumptions on l and the exact order of steps (see Chen et al. [2013] for a detailed description).”
A primal-dual algorithm with optimal stepsizes and its application in decentralized consensus optimization (2017, methodology): “When ∇ l ∗ ≡ 0 and P = D = I , the iteration reduces to (4), which is an existing primal-dual algorithm proposed in [5,9,16].”