Two New Inertial Algorithms for Solving Variational Inequalities in Reflexive Banach Spaces

DOI10.1080/01630563.2021.2006692OpenAlexW4200196798MaRDI QIDQ5069195

Pongsakorn Sunthrayuth, Prasit Cholamjiak, Truong Minh Tuyen, Simeon Reich

Publication date: 8 April 2022

Published in: Numerical Functional Analysis and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/01630563.2021.2006692

zbMATH Keywords

strong convergencereflexive Banach spaceextragradient methodBregman projectionLegendre function

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Equations involving nonlinear operators (general) (47J05) Fixed-point theorems (47H10) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09)

Related Items

Inertial Extragradient Method for Solving Variational Inequality and Fixed Point Problems of a Bregman Demigeneralized Mapping in a Reflexive Banach Spaces, An inertial method for split equality common \(f, g\)-fixed point problems of \(f, g\)-pseudocontractive mappings in reflexive real Banach spaces, On some novel methods for solving the generalized Fermat-Torricelli problem in Hilbert spaces, An improved subgradient extragradient method with two different parameters for solving variational inequalities in reflexive Banach spaces, An inertial self-adaptive iterative algorithm for finding the common solutions to split feasibility and fixed point problems in specific Banach spaces, Novel inertial methods for fixed point problems in reflexive Banach spaces with applications, A new Halpern-type Bregman projection method for solving variational inequality problems in reflexive Banach space, Inertial hybrid gradient method with adaptive step size for variational inequality and fixed point problems of multivalued mappings in Banach spaces, Inertial‐like Bregman projection method for solving systems of variational inequalities, Relaxed double inertial Tseng's extragradient method for solving non-Lipschitz split monotone variational inclusion problems with fixed point constraints, Fast relaxed inertial Tseng's method-based algorithm for solving variational inequality and fixed point problems in Hilbert spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The subgradient extragradient method for solving variational inequalities in Hilbert space
• Two strong convergence theorems for Bregman strongly nonexpansive operators in reflexive Banach spaces
• Bregman distances and Chebyshev sets
• Totally convex functions for fixed points computation and infinite dimensional optimization
• Weak and strong convergence theorems for variational inequality problems
• Strong convergence for gradient projection method and relatively nonexpansive mappings in Banach spaces
• Convergence of a splitting inertial proximal method for monotone operators
• Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups.
• Weak convergence of iterative methods for solving quasimonotone variational inequalities
• Inertial iterative algorithms for common solution of variational inequality and system of variational inequalities problems
• Modified Tseng's splitting algorithms for the sum of two monotone operators in Banach spaces
• New Bregman projection methods for solving pseudo-monotone variational inequality problem
• Single projection algorithm for variational inequalities in Banach spaces with application to contact problem
• A strong convergence theorem for Tseng's extragradient method for solving variational inequality problems
• Shrinking projection methods for accelerating relaxed inertial Tseng-type algorithm with applications
• Strong convergence theorems by hybrid methods for families of nonexpansive mappings in Hilbert spaces
• Bregman distances, totally convex functions, and a method for solving operator equations in Banach spaces
• Two Strong Convergence Theorems for a Proximal Method in Reflexive Banach Spaces
• A variant of korpelevich’s method for variational inequalities with a new search strategy
• ESSENTIAL SMOOTHNESS, ESSENTIAL STRICT CONVEXITY, AND LEGENDRE FUNCTIONS IN BANACH SPACES
• First-Order Methods in Optimization
• An Introduction to Nonlinear Analysis and Fixed Point Theory
• Re-examination of Bregman functions and new properties of their divergences
• Metric and Generalized Projection Operators in Banach Spaces: Properties and Applications
• A Modified Forward-Backward Splitting Method for Maximal Monotone Mappings
• Improved inertial extragradient methods for solving pseudo-monotone variational inequalities
• Modified Tseng's extragradient methods for variational inequality on Hadamard manifolds
• Modified Tseng's extragradient methods for solving pseudo-monotone variational inequalities
• The Burbea-Rao and Bhattacharyya Centroids
• Accelerated hybrid and shrinking projection methods for variational inequality problems
• Some methods of speeding up the convergence of iteration methods
• Generalized Projection Operators in Banach Spaces: Properties and Applications
• An inertial proximal method for maximal monotone operators via discretization of a nonlinear oscillator with damping
• Improvements of some projection methods for monotone nonlinear variational inequalities