Applying FISTA to optimization problems (with or) without minimizers

Bauschke, Heinz H.; Bùi, Minh N.; Wang, Xianfu

doi:10.1007/s10107-019-01415-x

Cited by 9 publications

(4 citation statements)

References 22 publications

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“…The condition on the sequence tt k u kě1 which we will assume in the next proposition in order to guarantee boundedness for the sequences generated by Algorithm ? ?has been proposed in [4]. Later we will see that it is satisfied by the three classical inertial parameters rules by Nesterov, Chambolle-Dossal and Attouch-Cabot.…”

Section: On the Boundedness Of The Sequencesmentioning

confidence: 76%

Fast Augmented Lagrangian Method in the convex regime with convergence guarantees for the iterates

Boţ¹,

Csetnek²,

Nguyen³

2021

Preprint

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This work aims to minimize a continuously differentiable convex function with Lipschitz continuous gradient under linear equality constraints. The proposed inertial algorithm results from the discretization of the second-order primal-dual dynamical system with asymptotically vanishing damping term addressed by Bot ¸and Nguyen in [8], and it is formulated in terms of the Augmented Lagrangian associated with the minimization problem. The general setting we consider for the inertial parameters covers the three classical rules by Nesterov, Chambolle-Dossal and Attouch-Cabot used in the literature to formulate fast gradient methods. For these rules, we obtain in the convex regime convergence rates of order O `1{k 2 ˘for the primal-dual gap, the feasibility measure, and the objective function value. In addition, we prove that the generated sequence of primal-dual iterates converges to a primal-dual solution in a general setting that covers the two latter rules. This is the first result which provides the convergence of the sequence of iterates generated by a fast algorithm for linearly constrained convex optimization problems without additional assumptions such as strong convexity. We also emphasize that all convergence results of this paper are compatible with the ones obtained in [8] in the continuous setting.

show abstract

Section: On the Boundedness Of The Sequencesmentioning

confidence: 76%

Fast Augmented Lagrangian Method in the convex regime with convergence guarantees for the iterates

Boţ¹,

Csetnek²,

Nguyen³

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…The condition on the sequence {t k } k 1 which we will assume in the next proposition in order to guarantee boundedness for the sequences generated by Algorithm 1 has been proposed in [4]. Later we will see that it is satisfied by the three classical inertial parameters rules by Nesterov, Chambolle-Dossal and Attouch-Cabot.…”

Section: On the Boundedness Of The Sequencesmentioning

confidence: 98%

Fast Augmented Lagrangian Method in the convex regime with convergence guarantees for the iterates

2022

View full text Add to dashboard Cite

This work aims to minimize a continuously differentiable convex function with Lipschitz continuous gradient under linear equality constraints. The proposed inertial algorithm results from the discretization of the second-order primal-dual dynamical system with asymptotically vanishing damping term addressed by Boţ and Nguyen (J. Differential Equations 303:369–406, 2021), and it is formulated in terms of the Augmented Lagrangian associated with the minimization problem. The general setting we consider for the inertial parameters covers the three classical rules by Nesterov, Chambolle–Dossal and Attouch–Cabot used in the literature to formulate fast gradient methods. For these rules, we obtain in the convex regime convergence rates of order $${\mathcal {O}}\left( 1/k^{2} \right) $$ O 1 / k 2 for the primal-dual gap, the feasibility measure, and the objective function value. In addition, we prove that the generated sequence of primal-dual iterates converges to a primal-dual solution in a general setting that covers the two latter rules. This is the first result which provides the convergence of the sequence of iterates generated by a fast algorithm for linearly constrained convex optimization problems without additional assumptions such as strong convexity. We also emphasize that all convergence results of this paper are compatible with the ones obtained in Boţ and Nguyen (J. Differential Equations 303:369–406, 2021) in the continuous setting.

show abstract

“…The theory can be applied in variety of fields like machine learning, game theory, economics, control theory among others, see Refs. [ [1] , [2] , [3] , [4] , [5] , [6] , [7] , [8] , [9] , [10] ] for more details.…”

Section: Introductionmentioning

confidence: 99%

An innovative inertial extra-proximal gradient algorithm for solving convex optimization problems with application to image and signal processing

Olilima,

Mogbademu,

Memon

et al. 2023

Heliyon

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Applying FISTA to optimization problems (with or) without minimizers

Cited by 9 publications

References 22 publications

Fast Augmented Lagrangian Method in the convex regime with convergence guarantees for the iterates

Fast Augmented Lagrangian Method in the convex regime with convergence guarantees for the iterates

Fast Augmented Lagrangian Method in the convex regime with convergence guarantees for the iterates

An innovative inertial extra-proximal gradient algorithm for solving convex optimization problems with application to image and signal processing

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