An inertial forward-backward-forward primal-dual splitting algorithm for solving monotone inclusion problems

Boţ, Radu Ioan; Csetnek, Ernö Robert

doi:10.1007/s11075-015-0007-5

Cited by 122 publications

(41 citation statements)

References 31 publications

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“…Starting from the paper [47], it is observed that using some inertia for the optimization algorithm often accelerates the latter. Later, papers [1,14,32,40] extend this idea to a more general case with monotone operators. In our case it will be in particular interesting to do so, since our scheme z k+1 = prox λg (z k − λF (z k )) (82)…”

Section: Beyond Monotonicitymentioning

confidence: 99%

Golden ratio algorithms for variational inequalities

2019

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The paper presents a fully adaptive algorithm for monotone variational inequalities. In each iteration the method uses two previous iterates for an approximation of the local Lipschitz constant without running a linesearch. Thus, every iteration of the method requires only one evaluation of a monotone operator F and a proximal mapping g. The operator F need not be Lipschitz continuous, which also makes the algorithm interesting in the area of composite minimization. The method exhibits an ergodic O(1/k) convergence rate and R-linear rate under an error bound condition. We discuss possible applications of the method to fixed point problems as well as its different generalizations.Keywords. variational inequality · first-order methods · linesearch · saddle point problem · composite minimization · fixed point problem MSC2010. 47J20, 65K10, 65K15, 65Y20, 90C33

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Section: Beyond Monotonicitymentioning

confidence: 99%

Golden ratio algorithms for variational inequalities

2019

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“…It is also well known that iterative methods with inertial effects may lead to a considerable improvement of the convergence behavior of the method. We refer the reader to [4,11,[14][15][16]24] and the references therein for more insight into this research topic. Of course, one way to address this research direction is to consider the inertial effects of the proposed algorithms and to analyze their convergence results.…”

Section: Hierarchical Minimization Problemmentioning

confidence: 99%

Generalized forward–backward splitting with penalization for monotone inclusion problems

Nimana

Petrot

2018

J Glob Optim

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We introduce a generalized forward-backward splitting method with penalty term for solving monotone inclusion problems involving the sum of a finite number of maximally monotone operators and the normal cone to the nonempty set of zeros of another maximally monotone operator. We show weak ergodic convergence of the generated sequence of iterates to a solution of the considered monotone inclusion problem, provided that the condition corresponding to the Fitzpatrick function of the operator describing the set of the normal cone is fulfilled. Under strong monotonicity of an operator, we show strong convergence of the iterates. Furthermore, we utilize the proposed method for minimizing a largescale hierarchical minimization problem concerning the sum of differentiable and nondifferentiable convex functions subject to the set of minima of another differentiable convex function. We illustrate the functionality of the method through numerical experiments addressing constrained elastic net and generalized Heron location problems.Keywords Monotone operator · monotone inclusion · hierarchical optimization · forward-backward algorithm Mathematics Subject Classification (2010) 47H05 · 65K05 · 65K10 · 90C25

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“…The following results is a very useful tool in the convergence analysis of inertial algorithms (see [1,2,20]). …”

Section: Lemma 3 Let U ∈ Smentioning

confidence: 99%

An Inertial Proximal-Gradient Penalization Scheme for Constrained Convex Optimization Problems

2017

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We propose a proximal-gradient algorithm with penalization terms and inertial and memory effects for minimizing the sum of a proper, convex, and lower semicontinuous and a convex differentiable function subject to the set of minimizers of another convex differentiable function. We show that, under suitable choices for the step sizes and the penalization parameters, the generated iterates weakly converge to an optimal solution of the addressed bilevel optimization problem, while the objective function values converge to its optimal objective value.

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An inertial forward-backward-forward primal-dual splitting algorithm for solving monotone inclusion problems

Cited by 122 publications

References 31 publications

Golden ratio algorithms for variational inequalities

Golden ratio algorithms for variational inequalities

Generalized forward–backward splitting with penalization for monotone inclusion problems

An Inertial Proximal-Gradient Penalization Scheme for Constrained Convex Optimization Problems

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