Convergence Analysis and Applications of the Glowinski–Le Tallec Splitting Method for Finding a Zero of the Sum of Two Maximal Monotone Operators

Haubruge, Sylvianne; Nguyen, Van Hien; Strodiot, Jean Jacques

doi:10.1023/a:1022646327085

Cited by 84 publications

(53 citation statements)

References 19 publications

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“…1 Department of Mathematics, University of Lagos, Akoka, Yaba, Lagos, Nigeria. 2 General Studies Department, Federal School of Surveying, Oyo, Oyo, Nigeria.…”

Section: Competing Interestsmentioning

confidence: 99%

Strong convergence and stability of Kirk-multistep-type iterative schemes for contractive-type operators

Akewe

Okeke

Olayiwola

2014

Fixed Point Theory Appl

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In this paper, we introduce Kirk-multistep and Kirk-multistep-SP iterative schemes and prove their strong convergences and stabilities for contractive-type operators in normed linear spaces. By taking numerical examples, we compare the convergence speed of our schemes (Kirk-multistep-SP iterative schemes) with the others (Kirk-SP, Kirk-Noor, Kirk-Ishikawa, Kirk-Mann and Kirk iterative schemes) for this class of operators. Our results generalize and extend most convergence and stability results in the literature. MSC: 47H09; 47H10

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“…1 Department of Mathematics, University of Lagos, Akoka, Yaba, Lagos, Nigeria. 2 General Studies Department, Federal School of Surveying, Oyo, Oyo, Nigeria.…”

Section: Competing Interestsmentioning

confidence: 99%

Strong convergence and stability of Kirk-multistep-type iterative schemes for contractive-type operators

Akewe

Okeke

Olayiwola

2014

Fixed Point Theory Appl

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“…The mature methods are least square method [6] and improved least square method [7]. Other methods include error prediction estimation method [8], IV estimation method [9] and the mathematical approximation method, such as the forward-backward method [10], Yule-Walker method, Burg method [11], the geometric lattice method [12]. Among them, IV estimation method is simple at some extent, and it can be used under many circumstances [13].The unbiased estimation value can be obtained, when the residuals are auto-regression [14,15].…”

Section: Estimation Of the Parametersmentioning

confidence: 99%

Extending Instrumental Variable Method for Effective Economic Modelling

Zheng¹,

Jin²,

Wen³

2012

IJCNS

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Economic modeling that yields practical value must cater for effects caused by exogenous variables. AutoRegressive eXogenous approach (ARX) has been widely used in regional economic studies. Instrumental Variable Method is regarded as a preferential method to parametric estimation in ARX modeling. However, traditional instrumental variable methods can only handle single variable which has limited its capability. This paper presents an extended instrumental variable method (EIVM) which is based on multiple variables. This provides the capability of taking into account of exogenous variables and reflects better the economic activities. A case study is conducted, which illustrates the application of the EIVM in modeling Northeastern economy in China.

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“…Glowinski and Le Tallec [9] used three-step iterative algorithms to find the approximate solutions of the elastoviscoplasticity problem, liquid crystal theory, and eigenvalue computation, and they showed that three-step approximations perform better numerically. Haubruge et al [11] studied the convergence analysis of three-step iterative algorithms of Glowinski and Le Tallec [9] and applied these algorithms to obtain new splitting-type algorithms for solving variational inequalities, separable convex programming, and minimization of a sum of convex functions. They also proved that three-step iterations lead to highly parallelized algorithms under certain conditions.…”

Section: Introductionmentioning

confidence: 99%

“…It has been shown in [11,21,22] that three step iterative algorithms are a natural generalization of the splitting methods for solving partial differential equations (inclusions). For applications of splitting and decomposition methods, see [9,11,21,22] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

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Convergence and stability of a three-step iterative algorithm for a general quasi-variational inequality problem

Kazmi

Bhat

2006

Fixed Point Theory Appl.

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We consider a general quasi-variational inequality problem involving nonlinear, nonconvex and nondifferentiable term in uniformly smooth Banach space. Using retraction mapping and fixed point method, we study the existence of solution of general quasivariational inequality problem and discuss the convergence analysis and stability of a three-step iterative algorithm for general quasi-variational inequality problem. The theorems presented in this paper generalize, improve, and unify many previously known results in the literature.

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Convergence Analysis and Applications of the Glowinski–Le Tallec Splitting Method for Finding a Zero of the Sum of Two Maximal Monotone Operators

Cited by 84 publications

References 19 publications

Strong convergence and stability of Kirk-multistep-type iterative schemes for contractive-type operators

Strong convergence and stability of Kirk-multistep-type iterative schemes for contractive-type operators

Extending Instrumental Variable Method for Effective Economic Modelling

Convergence and stability of a three-step iterative algorithm for a general quasi-variational inequality problem

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