Operator Splitting Performance Estimation: Tight Contraction Factors and Optimal Parameter Selection

Ryu, Ernest K.; Taylor, Adrien; Bergeling, Carolina; Giselsson, Pontus

doi:10.1137/19m1304854

Cited by 43 publications

(37 citation statements)

References 52 publications

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“…The authors of [35] introduced tightness guarantees for smooth (strongly) convex optimization, and for larger classes of problems in [36] (where a list of sufficient conditions for applying the methodology is provided). It was also used to deal with nonsmooth problems [11,36], monotone inclusions and variational inequalities [16,17,21,31], and even to study fixed-point iterations of non-expansive operators [25]. Fixed-step gradient descent was among the first algorithms to be studied with this methodology in different settings: for (possibly composite) smooth (possibly strongly) convex optimization [14,15,35,36], and its line-search version was studied using the same methodology in [22].…”

mentioning

confidence: 99%

Worst-Case Convergence Analysis of Inexact Gradient and Newton Methods Through Semidefinite Programming Performance Estimation

Klerk¹,

Glineur²,

Taylor³

2020

SIAM J. Optim.

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mentioning

confidence: 99%

Worst-Case Convergence Analysis of Inexact Gradient and Newton Methods Through Semidefinite Programming Performance Estimation

Klerk¹,

Glineur²,

Taylor³

2020

SIAM J. Optim.

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“…Not only do these illustrations provide intuition. Indeed, it is a straightforward consequence of, e.g., [ 24 , 25 ] that for compositions of two operator classes that admit I-N decompositions, there always exists a 2D-worst case. Hence, if the 2D illustration implies that the composition class admits a specific -I-N decomposition, so does the full operator class.…”

Section: Graphical Characterizationsmentioning

confidence: 99%

On compositions of special cases of Lipschitz continuous operators

Giselsson

Moursi

2021

Fixed Point Theory Algorithms Sci Eng

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Many iterative optimization algorithms involve compositions of special cases of Lipschitz continuous operators, namely firmly nonexpansive, averaged, and nonexpansive operators. The structure and properties of the compositions are of particular importance in the proofs of convergence of such algorithms. In this paper, we systematically study the compositions of further special cases of Lipschitz continuous operators. Applications of our results include compositions of scaled conically nonexpansive mappings, as well as the Douglas–Rachford and forward–backward operators, when applied to solve certain structured monotone inclusion and optimization problems. Several examples illustrate and tighten our conclusions.

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“…Operator regression is a recent and at the same time old topic. We are going to build on the recent work [41] and the F.A. Valentine's 1945 paper [42].…”

Section: Related Workmentioning

confidence: 99%

OpReg-Boost: Learning to Accelerate Online Algorithms with Operator Regression

Bastianello¹,

Simonetto²,

Dall’Anese³

2021

Preprint

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This paper presents a new regularization approach -termed OpReg-Boost -to boost the convergence and lessen the asymptotic error of online optimization and learning algorithms. In particular, the paper considers online algorithms for optimization problems with a time-varying (weakly) convex composite cost. For a given online algorithm, OpReg-Boost learns the closest algorithmic map that yields linear convergence; to this end, the learning procedure hinges on the concept of operator regression. We show how to formalize the operator regression problem and propose a computationally-efficient Peaceman-Rachford solver that exploits a closed-form solution of simple quadratically-constrained quadratic programs (QCQPs). Simulation results showcase the superior properties of OpReg-Boost w.r.t. the more classical forward-backward algorithm, FISTA, and Anderson acceleration, and with respect to its close relative convex-regression-boost (CvxReg-Boost) which is also novel but less performing.

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Operator Splitting Performance Estimation: Tight Contraction Factors and Optimal Parameter Selection

Cited by 43 publications

References 52 publications

Worst-Case Convergence Analysis of Inexact Gradient and Newton Methods Through Semidefinite Programming Performance Estimation

Worst-Case Convergence Analysis of Inexact Gradient and Newton Methods Through Semidefinite Programming Performance Estimation

On compositions of special cases of Lipschitz continuous operators

OpReg-Boost: Learning to Accelerate Online Algorithms with Operator Regression

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