The viscosity approximation forward-backward splitting method for zeros of the sum of monotone operators

DOI10.1155/2016/2371857zbMath1470.65109OpenAlexW2305020619WikidataQ59121515 ScholiaQ59121515MaRDI QIDQ1669217

Oganeditse Aaron Boikanyo

Publication date: 30 August 2018

Published in: Abstract and Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2016/2371857

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Numerical solutions to equations with nonlinear operators (65J15)

Related Items

Convergence theorems for split feasibility problems on a finite sum of monotone operators and a family of nonexpansive mappings ⋮ Strong convergence theorems for a class of split feasibility problems and fixed point problem in Hilbert spaces ⋮ On a system of monotone variational inclusion problems with fixed-point constraint ⋮ Iterative methods for zeros of a monotone variational inclusion in Hilbert spaces ⋮ Weak convergence theorems for split feasibility problems on zeros of the sum of monotone operators and fixed point sets in Hilbert spaces ⋮ Modified Inertial Algorithms for a Class of Split Feasibility Problems and Fixed Point Problems in Hilbert Spaces ⋮ A strong convergence algorithm for a fixed point constrained split null point problem ⋮ Forward-backward splitting algorithm for fixed point problems and zeros of the sum of monotone operators ⋮ Finding a solution of split null point of the sum of monotone operators without prior knowledge of operator norms in Hilbert spaces ⋮ New strong convergence method for the sum of two maximal monotone operators ⋮ Strong convergence for a modified forward-backward splitting method in Banach spaces ⋮ On the inertial forward-backward splitting technique for solving a system of inclusion problems in Hilbert spaces

Cites Work

• Forward-backward splitting methods for accretive operators in Banach spaces
• Strong convergence theorems for maximal monotone operators with nonlinear mappings in Hilbert spaces
• Four parameter proximal point algorithms
• Strong convergence of a proximal point algorithm with general errors
• A regularization method for the proximal point algorithm
• On convergence criteria of generalized proximal point algorithms
• Strong convergence of projected subgradient methods for nonsmooth and nonstrictly convex minimization
• Ergodic convergence to a zero of the sum of monotone operators in Hilbert space
• Strong convergence of a splitting proximal projection method for the sum of two maximal monotone operators
• Approximating solutions of maximal monotone operators in Hilbert spaces
• On the contraction-proximal point algorithms with multi-parameters
• Forcing strong convergence of proximal point iterations in a Hilbert space
• The contraction-proximal point algorithm with square-summable errors
• A family of projective splitting methods for the sum of two maximal monotone operators
• Iterative Algorithms for Nonlinear Operators
• General Projective Splitting Methods for Sums of Maximal Monotone Operators
• On the Convergence of the Proximal Point Algorithm for Convex Minimization
• Monotone Operators and the Proximal Point Algorithm
• Operator-Splitting Methods for Monotone Affine Variational Inequalities, with a Parallel Application to Optimal Control
• A Modified Forward-Backward Splitting Method for Maximal Monotone Mappings
• Convergence of the generalized contraction-proximal point algorithm in a Hilbert space
• On the Maximality of Sums of Nonlinear Monotone Operators
• Combining The Proximal Algorithm And Tikhonov Regularization
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item