Application of a new accelerated algorithm to regression problems

Dixit, Avinash; Sahu, D. R.; Singh, Amit; Som, Tanmoy

doi:10.1007/s00500-019-03984-7

Cited by 16 publications

(11 citation statements)

References 31 publications

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“…From Proposition 3.2, we conclude that inclusion problem (3.1) can be solved by finding fixed points of the operator J A,B λ ,M . In the light of this fact and motivated by [23], we propose the following algorithm.…”

Section: Resultsmentioning

confidence: 99%

An accelerated forward-backward splitting algorithm for solving inclusion problems with applications to regression and link prediction problems

2021

J. Nonlinear Var. Anal.

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The forward-backward method is a very popular approach to solve composite inclusion problems. In this paper, we propose a novel accelerated forward-backward algorithm to obtain the vanishing point of sum of two operators in which one is maximal monotone and other is M-cocoercive, where M is a linear bounded operator on underlying spaces. Our proposed algorithm is more general than previously known algorithms. We study the convergence behavior of proposed algorithm under mild assumptions in the framework of real Hilbert spaces. We employ our model to solve regression problems and link prediction problems for high dimensional datasets and conduct numerical experiments to support our results. This model improves convergence speed and accuracy in respective problems. We also conduct numerical experiments to support our results.

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Section: Resultsmentioning

confidence: 99%

An accelerated forward-backward splitting algorithm for solving inclusion problems with applications to regression and link prediction problems

2021

J. Nonlinear Var. Anal.

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“…) and θ n = .9δ(ε) for algorithms RIM-KEM(31) and RIM-SEM(37), where δ is defined in (12) and ε = (1 + κ E − b)/b. • α n = b = .961(1 + κ E ) and θ n = .9δ(E) in algorithms RInS-KEM (33) and RInS-SEM (39),…”

Section: Example 41 Letmentioning

confidence: 99%

A unified framework for three accelerated extragradient methods and further acceleration for variational inequality problems

Sahu

2021

Preprint

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The main strategy of this paper is intended to speed up the convergence of the inertial Mann iterative method and further speed up it through the normal S-iterative method for a certain class of nonexpansive type operators that are linked with variational inequality problems. Our new convergence theory permits us to settle down the difficulty of unification of Korpelevich's extragradient method, Tseng's extragardient method, and subgardient extragardient method for solving variational inequality problems through an auxiliary algorithmic operator, which is associated with seed operator. The paper establishes an interesting fact that the relaxed inertial normal S-iterative extragradient methods do influence much more on convergence behaviour. Finally, the numerical experiments are carried out to illustrate that the relaxed inertial iterative methods, in particular the relaxed inertial normal S-iterative extragradient methods, may have a number of advantages over other methods in computing solutions of variational inequality problems in many cases.

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“…Fixed points iterative methods play a vital role in designing many iterative methods (Ref. [21,10]). For example, Krasnoselskii-Mann (KM) iterative method introduced in [42,35] for solving fixed point of quasi-nonexpansive mappings T given by the following scheme…”

Section: Introductionmentioning

confidence: 99%

An inertial iterative scheme for solving variational inclusion with application to Nash-Cournot equilibrium and image restoration problems

Abubakar¹,

Garba²,

Abdullahi³

et al. 2021

CJM

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Variational inclusion is an important general problem consisting of many useful problems like variational inequality, minimization problem and nonlinear monotone equations. In this article, a new scheme for solving variational inclusion problem is proposed and the scheme uses inertial and relaxation techniques. Moreover, the scheme is self adaptive, that is, the stepsize does not depend on the factorial constants of the underlying operator, instead it can be computed using a simple updating rule. Weak convergence analysis of the iterates generated by the new scheme is presented under mild conditions. In addition, schemes for solving variational inequality problem and split feasibility problem are derived from the proposed scheme and applied in solving Nash-Cournot equilibrium problem and image restoration. Experiments to illustrate the implementation and potential applicability of the proposed schemes in comparison with some existing schemes in the literature are presented.

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Application of a new accelerated algorithm to regression problems

Cited by 16 publications

References 31 publications

An accelerated forward-backward splitting algorithm for solving inclusion problems with applications to regression and link prediction problems

An accelerated forward-backward splitting algorithm for solving inclusion problems with applications to regression and link prediction problems

A unified framework for three accelerated extragradient methods and further acceleration for variational inequality problems

An inertial iterative scheme for solving variational inclusion with application to Nash-Cournot equilibrium and image restoration problems

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