Journal ArticleDOI
Modified inertial subgradient extragradient method with self adaptive stepsize for solving monotone variational inequality and fixed point problems
TLDR
In this article, a monotone and Lipschitz continuous variational inequality and fixed point problems are studied on a level set of a convex function in the setting of Hilbert space.Abstract:
In this paper, we study a classical monotone and Lipschitz continuous variational inequality and fixed point problems defined on a level set of a convex function in the setting of Hilbert space. We...read more
Citations
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Halpern-type iterative process for solving split common fixed point and monotone variational inclusion problem between Banach spaces
TL;DR: A Halpern-type algorithm with two self-adaptive stepsizes for obtaining solution of the split common fixed point and monotone variational inclusion problem in uniformly convex and 2-uniformly smooth Banach spaces is proposed and strong convergence theorem for the algorithm is proved.
Journal ArticleDOI
Inertial methods for finding minimum-norm solutions of the split variational inequality problem beyond monotonicity
TL;DR: This paper presents two new methods with inertial steps for solving the split variational inequality problems in real Hilbert spaces without any product space formulation and proves that the sequence generated by these methods converges strongly to a minimum-norm solution of the problem when the operators are pseudomonotone and Lipschitz continuous.
Journal ArticleDOI
An inertial method for solving generalized split feasibility problems over the solution set of monotone variational inclusions
TL;DR: In this paper, an inertial extrapolation method for solving generalized split feasibility problems over the solution set of monotone variational inclusion problems in real Hilbert space is proposed. But this method is not suitable for real Hilbert spaces.
Journal ArticleDOI
An iterative algorithm for solving variational inequality, generalized mixed equilibrium, convex minimization and zeros problems for a class of nonexpansive-type mappings
TL;DR: In this paper, an iterative scheme which combines the inertial subgradient extragradient method with viscosity technique and with self-adaptive stepsize was proposed.
Journal ArticleDOI
Inertial shrinking projection algorithm with self-adaptive step size for split generalized equilibrium and fixed point problems for a countable family of nonexpansive multivalued mappings
References
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A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
Amir Beck,Marc Teboulle +1 more
TL;DR: A new fast iterative shrinkage-thresholding algorithm (FISTA) which preserves the computational simplicity of ISTA but with a global rate of convergence which is proven to be significantly better, both theoretically and practically.
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An introduction to variational inequalities and their applications
TL;DR: In this paper, the SIAM edition Preface Glossary of notations Introduction Part I. Variational Inequalities in Rn Part II. Free Boundary Problems Governed by Elliptic Equations and Systems Part VII. A One Phase Stefan Problem Bibliography Index.
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Some methods of speeding up the convergence of iteration methods
TL;DR: In this article, the authors consider the problem of minimizing the differentiable functional (x) in Hilbert space, so long as this problem reduces to the solution of the equation grad(x) = 0.
Journal ArticleDOI
Mathematical Analysis and Numerical Methods for Science and Technology
TL;DR: These six volumes as mentioned in this paper compile the mathematical knowledge required by researchers in mechanics, physics, engineering, chemistry and other branches of application of mathematics for the theoretical and numerical resolution of physical models on computers.
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Fundamentals of Convex Analysis
TL;DR: In this paper, the authors define and define Convex functions, Sublinear Functions and Sublinearity and Support Functions of a Nonempty Set Correspondence between ConveX Sets and SubLinear Functions, and Subdifferentials of Finite Functions.