FOM – a MATLAB toolbox of first-order methods for solving convex optimization problems

Beck, Amir; Guttmann‐Beck, Nili

doi:10.1080/10556788.2018.1437159

Cited by 32 publications

(18 citation statements)

References 13 publications

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“…4.3). We use the FOM Solver [3] to effectively calculate the projections onto C and T n . All the programs are implemented in MATLAB 2018a on a personal computer.…”

Section: Numerical Experimentsmentioning

confidence: 99%

Strong convergence of inertial projection and contraction methods for pseudomonotone variational inequalities with applications to optimal control problems

Tan

Yao

2021

J Glob Optim

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This paper investigates some inertial projection and contraction methods for solving pseudomonotone variational inequality problems in real Hilbert spaces. The algorithms use a new non-monotonic step size so that they can work without the prior knowledge of the Lipschitz constant of the operator. Strong convergence theorems of the suggested algorithms are obtained under some suitable conditions. Some numerical experiments in finite-and infinite-dimensional spaces and applications in optimal control problems are implemented to demonstrate the performance of the suggested schemes and we also compare them with several related results.

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“…4.3). We use the FOM Solver [3] to effectively calculate the projections onto C and T n . All the programs are implemented in MATLAB 2018a on a personal computer.…”

Section: Numerical Experimentsmentioning

confidence: 99%

Strong convergence of inertial projection and contraction methods for pseudomonotone variational inequalities with applications to optimal control problems

Tan

Yao

2021

J Glob Optim

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“…3.2). We use the FOM Solver [35] to solve the projections involved in all algorithms. All the programs were implemented in MATLAB 2018a on a Intel(R) Core(TM) i5-8250U CPU @ 1.60GHz computer with RAM 8.00 GB.…”

Section: Numerical Examplesmentioning

confidence: 99%

Inertial extragradient methods for solving pseudomonotone variational inequalities with non-Lipschitz mappings and their optimization applications

2021

Appl. Set-Valued Anal. Optim.

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In this paper, four extragradient-type algorithms with inertial terms are presented for solving the variational inequality problem with a pseudomonotone and non-Lipschitz continuous operator in real Hilbert spaces. Strong convergence theorems of the suggested methods are established under some suitable conditions imposed on the parameters. Finally, several computational tests and applications in optimal control problems are given to illustrate the efficiency and advantages of the proposed iterative schemes over some known ones.

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“…In this section, we use some numerical experiments to illustrate the computational performance of our proposed Algorithm (3.1) and Algorithm (4.1) by comparing them with the Algorithm (1.7) in [10]. It should be pointed out that we use the FOM Solver [4] and the function fmincon in MATLAB Optimization Toolbox to effectively calculate the projections onto C n ∩ Q n and C n+1 . All the programs are performed in MATLAB2018a on a PC Desktop Intel(R) Core(TM) i5-8250U CPU @ 1.60GHz 1.800 GHz, RAM 8.00 GB.…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…4) where B : C ×C → R is a bifunction and A : C → H is a nonlinear mapping. Let Ω be the solution set of MEP(5.4).…”

mentioning

confidence: 99%

Strong convergence of two inertial projection algorithms in Hilbert spaces

2020

J. Appl. Numer. Optim.

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In this paper, we propose two inertial projection algorithms for finding a common solution of monotone variational inclusions and hierarchical fixed point problems of nonexpansive mappings. We obtain two strong convergence theorems under some suitable conditions in Hilbert spaces. In addition, we also give numerical examples to compare our algorithms with the existing ones. Numerical results show that our proposed algorithms are efficient and robust.

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FOM – a MATLAB toolbox of first-order methods for solving convex optimization problems

Cited by 32 publications

References 13 publications

Strong convergence of inertial projection and contraction methods for pseudomonotone variational inequalities with applications to optimal control problems

Strong convergence of inertial projection and contraction methods for pseudomonotone variational inequalities with applications to optimal control problems

Inertial extragradient methods for solving pseudomonotone variational inequalities with non-Lipschitz mappings and their optimization applications

Strong convergence of two inertial projection algorithms in Hilbert spaces

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