The geometry of monotone operator splitting methods
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Publication:6598417
DOI10.1017/s0962492923000065zbMath1546.65037MaRDI QIDQ6598417
Publication date: 5 September 2024
Published in: Acta Numerica (Search for Journal in Brave)
Numerical mathematical programming methods (65K05) Convex programming (90C25) Optimality conditions and duality in mathematical programming (90C46) Variational inequalities (49J40) Monotone operators and generalizations (47H05) Iterative procedures involving nonlinear operators (47J25) Programming in abstract spaces (90C48) Numerical solutions to equations with nonlinear operators (65J15)
Related Items (2)
Proximity operators of perspective functions with nonlinear scaling ⋮ Integral resolvent and proximal mixtures
Cites Work
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- Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers
- Rare Feature Selection in High Dimensions
- A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
- Linear passive systems and maximal monotone mappings
- A primal-dual splitting method for convex optimization involving Lipschitzian, proximable and linear composite terms
- Iterative methods for fixed point problems in Hilbert spaces
- A Douglas-Rachford splitting method for solving equilibrium problems
- Primal-dual splitting algorithm for solving inclusions with mixtures of composite, Lipschitzian, and parallel-sum type monotone operators
- Proximal methods for the latent group lasso penalty
- A class of Fejér convergent algorithms, approximate resolvents and the hybrid proximal-extragradient method
- A primal-dual method of partial inverses for composite inclusions
- Compositions and convex combinations of averaged nonexpansive operators
- On the convergence of the iterates of the ``fast iterative shrinkage/thresholding algorithm
- Complementarity and variational inequalities in electronics
- Proximity for sums of composite functions
- Partial inverse of a monotone operator
- Fifty years of maximal monotonicity
- Dualization of signal recovery problems
- Alternating proximal algorithms for linearly constrained variational inequalities: application to domain decomposition for PDE's
- Consistent learning by composite proximal thresholding
- A three-operator splitting scheme and its optimization applications
- Variable metric quasi-Fejér monotonicity
- The asymptotic behavior of the composition of two resolvents
- A strongly convergent primal-dual method for nonoverlapping domain decomposition
- Subdivisions from primal and dual cones and polytopes
- An LS-free splitting method for composite mappings
- Composition duality principles for mixed variational inequalities
- Removing multiplicative noise by Douglas-Rachford splitting methods
- Conjugate duality in convex optimization
- Tikhonov-regularization of ill-posed linear operator equations on closed convex sets
- A cyclic projection algorithm via duality
- Monotone (nonlinear) operators in Hilbert space
- Newton's method for convex programming and Tschebyscheff approximation
- Ergodic convergence to a zero of the sum of monotone operators in Hilbert space
- Lectures on topics in finite element solution of elliptic problems. Notes by G. Vijayasundaram
- On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators
- An example concerning fixed points
- Quelques propriétés des opérateurs angle-bornes et n-cycliquement monotones
- A dual algorithm for the solution of nonlinear variational problems via finite element approximation
- A class of monotone operator functions related to electrical network theory
- Produits infinis de resolvantes
- Une méthode itérative de résolution d'une inéquation variationnelle
- A successive projection method
- Partial differential equations in the 20th century
- Composition duality and maximal monotonicity
- Proximal minimization algorithm with \(D\)-functions
- A proximal-based deomposition method for compositions method for convex minimization problems
- A general cone decomposition theory based on efficiency
- Dykstra's alternating projection algorithm for two sets
- A reduction method for variational inequalities
- Image denoising and decomposition with total variation minimization and oscillatory functions
- An algorithm for total variation minimization and applications
- Projection and proximal point methods: Convergence results and counterexamples.
- Sur la distribution des propriétés de voisinage des fonctions de variables reelles.
- Theorie der reellen Funktionen. Erster Band.
- Über die Lage der Nullstellen von Polynomen, die aus Minimumforderungen gewisser Arten entspringen.
- Sur les fonctions convexes et les inégalités entre les valeurs moyennes.
- Memoir on discontinuous functions.
- A hybrid approximate extragradient-proximal point algorithm using the enlargement of a maximal monotone operator
- On the regularization of the sum of two maximal monotone operators
- A simplified view of first order methods for optimization
- Monotone operator theory in convex optimization
- On the complexity of the projective splitting and Spingarn's methods for the sum of two maximal monotone operators
- Solving monotone stochastic variational inequalities and complementarity problems by progressive hedging
- On sums and convex combinations of projectors onto convex sets
- ADMM for the SDP relaxation of the QAP
- Proximal primal-dual best approximation algorithm with memory
- Smooth methods of multipliers for complementarity problems
- A projection method for least-squares solutions to overdetermined systems of linear inequalities
- Zur Theorie der nichtlinearen Integralgleichungen, Integralgleichungssysteme und allgemeinen Funktionalgleichungen
- A strongly convergent iterative solution of \(0 \in U(x)\) for a maximal monotone operator U in Hilbert space
- An alternating projection that does not converge in norm
- The primal Douglas-Rachford splitting algorithm for a class of monotone mappings with application to the traffic equilibrium problem
- A first-order primal-dual algorithm for convex problems with applications to imaging
- Proximal algorithms for multicomponent image recovery problems
- Regularizers for structured sparsity
- A splitting algorithm for dual monotone inclusions involving cocoercive operators
- Forcing strong convergence of proximal point iterations in a Hilbert space
- The distance between convex sets with Minkowski sum structure: application to collision detection
- Single-forward-step projective splitting: exploiting cocoercivity
- Solving composite fixed point problems with block updates
- Forward-backward-half forward dynamical systems for monotone inclusion problems with application to v-GNE
- Bregman forward-backward operator splitting
- Synthesis of recurrent neural dynamics for monotone inclusion with application to Bayesian inference
- Projective splitting with forward steps
- Projective splitting as a warped proximal algorithm
- Parallel random block-coordinate forward-backward algorithm: a unified convergence analysis
- A class of incrementally scattering-passive nonlinear systems
- Uniqueness of DRS as the 2 operator resolvent-splitting and impossibility of 3 operator resolvent-splitting
- On the complexity of a hybrid proximal extragradient projective method for solving monotone inclusion problems
- Deep neural network structures solving variational inequalities
- Warped proximal iterations for monotone inclusions
- Convergence of a relaxed inertial proximal algorithm for maximally monotone operators
- Fixing and extending some recent results on the ADMM algorithm
- The split feasibility problem with multiple output sets in Hilbert spaces
- A parallel proximal splitting method for disparity estimation from multicomponent images under illumination variation
- Convergence analysis for a primal-dual monotone + skew splitting algorithm with applications to total variation minimization
- Further applications of a splitting algorithm to decomposition in variational inequalities and convex programming
- Douglas-Rachford splitting and ADMM for pathological convex optimization
- Smoothing algorithms for computing the projection onto a Minkowski sum of convex sets
- Splitting Algorithms for the Sum of Two Nonlinear Operators
- Feedback Systems Described by Monotone Operators
- Convergence d'un schéma de minimisation alternée
- Applications of a Splitting Algorithm to Decomposition in Convex Programming and Variational Inequalities
- On the Convergence of the Proximal Point Algorithm for Convex Minimization
- Entropic Proximal Mappings with Applications to Nonlinear Programming
- Iteration methods for convexly constrained ill-posed problems in hilbert space
- A note regarding abstract operators and passive networks
- An iterative solution of a variational inequality for certain monotone operators in Hilbert space
- Monotone Operators and the Proximal Point Algorithm
- Augmented Lagrangians and Applications of the Proximal Point Algorithm in Convex Programming
- Modified Lagrangians in convex programming and their generalizations
- Application of the projected Landweber method to the estimation of the source time function in seismology
- Convergence Rates in Forward--Backward Splitting
- An Extension of the Auxiliary Problem Principle to Nonsymmetric Auxiliary Operators
- Nonlinear Monotone Networks
- Bregman Monotone Optimization Algorithms
- Dualization of Generalized Equations of Maximal Monotone Type
- Model Consistency of Partly Smooth Regularizers
- Quasi-Nonexpansive Iterations on the Affine Hull of Orbits: From Mann's Mean Value Algorithm to Inertial Methods
- Relatively Smooth Convex Optimization by First-Order Methods, and Applications
- Proximal Methods for Stationary Mean Field Games with Local Couplings
- Surpassing Gradient Descent Provably: A Cyclic Incremental Method with Linear Convergence Rate
- The Split Common Null Point Problem
- An iterative thresholding algorithm for linear inverse problems with a sparsity constraint
- Prox-Method with Rate of Convergence O(1/t) for Variational Inequalities with Lipschitz Continuous Monotone Operators and Smooth Convex-Concave Saddle Point Problems
- A class of decomposition methods for convex optimization and monotone variational inclusions via the hybrid inexact proximal point framework
- Solving monotone inclusions via compositions of nonexpansive averaged operators
- Forward-Backward-Half Forward Algorithm for Solving Monotone Inclusions
- Partial regularization of the sum of two maximal monotone operators
- Nonlinear Proximal Point Algorithms Using Bregman Functions, with Applications to Convex Programming
- Finite-Dimensional Variational Inequalities and Complementarity Problems
- A SPLITTING METHOD FOR COMPOSITE MAPPINGS
- Proximal Decomposition on the Graph of a Maximal Monotone Operator
- A Modified Forward-Backward Splitting Method for Maximal Monotone Mappings
- Rate of Convergence Analysis of Decomposition Methods Based on the Proximal Method of Multipliers for Convex Minimization
- Distributed Generalized Nash Equilibrium Seeking in Aggregative Games on Time-Varying Networks
- SURVEY: SIXTY YEARS OF DOUGLAS–RACHFORD
- Optimization for Data Analysis
- The Krasnosel'skiĭ-Mann Iterative Method
- A Variational Inequality Model for the Construction of Signals from Inconsistent Nonlinear Equations
- Analysis and Numerical Solution of a Modular Convex Nash Equilibrium Problem
- Multivariate Monotone Inclusions in Saddle Form
- Fixed Point Strategies in Data Science
- The Douglas--Rachford Algorithm Converges Only Weakly
- Proximal Activation of Smooth Functions in Splitting Algorithms for Convex Image Recovery
- Operator Splitting Performance Estimation: Tight Contraction Factors and Optimal Parameter Selection
- Algorithms and Convergence Results of Projection Methods for Inconsistent Feasibility Problems: A Review
- ADMM-Type Methods for Generalized Nash Equilibrium Problems in Hilbert Spaces
- Nonlinear Forward-Backward Splitting with Projection Correction
- Primal-Dual Decomposition by Operator Splitting and Applications to Image Deblurring
- The iterative solution of the equation $y \in x + Tx$ for a monotone operator $T$ in Hilbert space
- Dynamical Systems Coupled with Monotone Set-Valued Operators: Formalisms, Applications, Well-Posedness, and Stability
- A Distributed Flexible Delay-Tolerant Proximal Gradient Algorithm
- Modern regularization methods for inverse problems
- Convergence Rates for Projective Splitting
- Hypercomplex Tensor Completion via Convex Optimization
- Solving Coupled Composite Monotone Inclusions by Successive Fejér Approximations of their Kuhn--Tucker Set
- Primal-Dual Extragradient Methods for Nonlinear Nonsmooth PDE-Constrained Optimization
- Quelques résultats de Višik sur les problèmes elliptiques non linéaires par les méthodes de Minty-Browder
- Fast Gradient-Based Algorithms for Constrained Total Variation Image Denoising and Deblurring Problems
- Systems of Structured Monotone Inclusions: Duality, Algorithms, and Applications
- A Douglas--Rachford Type Primal-Dual Method for Solving Inclusions with Mixtures of Composite and Parallel-Sum Type Monotone Operators
- An Algorithm for Splitting Parallel Sums of Linearly Composed Monotone Operators, with Applications to Signal Recovery
- Signal Recovery by Proximal Forward-Backward Splitting
- Variable metric forward–backward splitting with applications to monotone inclusions in duality
- Stochastic Quasi-Fejér Block-Coordinate Fixed Point Iterations with Random Sweeping
- Proximité et dualité dans un espace hilbertien
- The closure of the numerical range contains the spectrum
- Multi-Valued Monotone Nonlinear Mappings and Duality Mappings in Banach Spaces
- Convex programming in Hilbert space
- Some methods of speeding up the convergence of iteration methods
- The Supporting Hyperplane Method for Unimodal Programming
- Stability Conditions for Systems with Monotone and Slope-Restricted Nonlinearities
- NON-LINEAR MONOTONE OPERATORS IN BANACH SPACES
- A Nonlinear Alternating Direction Method
- Convex Analysis
- The method of projections for finding the common point of convex sets
- A Weak-to-Strong Convergence Principle for Fejér-Monotone Methods in Hilbert Spaces
- ON A „MONOTONICITY” METHOD FOR THE SOLUTION OF NONLINEAR EQUATIONS IN BANACH SPACES
- A Descent Lemma Beyond Lipschitz Gradient Continuity: First-Order Methods Revisited and Applications
- An introduction to continuous optimization for imaging
- Monotone Operator Methods for Nash Equilibria in Non-potential Games
- Nonlinear networks. IIa
- Nonlinear networks. IIb
- Mean Value Methods in Iteration
- The Relaxation Method for Linear Inequalities
- The Relaxation Method for Linear Inequalities
- The method of steepest descent for non-linear minimization problems
- Nonlinear networks. I
- Nonlinear Differential Equations of Monotone Types in Banach Spaces
- Learning Maximally Monotone Operators for Image Recovery
- Degenerate Preconditioned Proximal Point Algorithms
- Convex analysis and monotone operator theory in Hilbert spaces
- Dissipative systems analysis and control. Theory and applications
- Facial reduction for symmetry reduced semidefinite and doubly nonnegative programs
- Proximal Splitting Algorithms for Convex Optimization: A Tour of Recent Advances, with New Twists
- A projective splitting method for monotone inclusions: iteration-complexity and application to composite optimization
- Circuit analysis using monotone+skew splitting
- Resolvent and proximal compositions
- Resolvent splitting for sums of monotone operators with minimal lifting
- Multidomain optimal control of variational subpotential mixed evolution inclusions
- Convergence of an asynchronous block-coordinate forward-backward algorithm for convex composite optimization
- Generalizations of the proximal method of multipliers in convex optimization
- Graphical Nonlinear System Analysis
- Monotone one-port circuits
- Perspective maximum likelihood-type estimation via proximal decomposition
- Projective splitting with forward steps only requires continuity
- Finding the forward-Douglas-Rachford-forward method
- A note on the forward-Douglas-Rachford splitting for monotone inclusion and convex optimization
- On the Douglas-Rachford algorithm
- Maximal monotonicity and cyclic monotonicity arising in nonsmooth Lur'e dynamical systems
- Asymmetric forward-backward-adjoint splitting for solving monotone inclusions involving three operators
- A simplified form of block-iterative operator splitting and an asynchronous algorithm resembling the multi-block alternating direction method of multipliers
- Forward-backward splitting with Bregman distances
- A primal Douglas-Rachford splitting method for the constrained minimization problem in compressive sensing
- Backward-forward algorithms for structured monotone inclusions in Hilbert spaces
- Asynchronous block-iterative primal-dual decomposition methods for monotone inclusions
- A random block-coordinate Douglas-Rachford splitting method with low computational complexity for binary logistic regression
- Notes on the difference of two monotone operators
- A family of projective splitting methods for the sum of two maximal monotone operators
- On the extension and the solution of nonlinear operator equations
- On optimal operation of communication nets
- Duality and stability in extremum problems involving convex functions
- Nonlinear semigroups in Hilbert space
- Multiplier and gradient methods
- Methodes itératives pour les équations et inéquations aux dérivées partielles non linéaires de type monotone. (Iteration methods for nonlinear equations and inequations with partial derivatives of monotone type)
- A note on segmenting Mann iterates
- The multiplier method of Hestenes and Powell applied to convex programming
- Dual variational inequalities
- Dual norms and image decomposition models
- Über Systeme von nichtlinearen Integralgleichungen.
- The solvability of non-linear functional equations
- On the monotonicity of the gradient of a convex function
- ADMM for monotone operators: convergence analysis and rates
- On generalized Nash games and variational inequalities
- A decomposition method for solving multicommodity network equilibria
- On the strong convergence of forward-backward splitting in reconstructing jointly sparse signals
- A primal-dual partial inverse algorithm for constrained monotone inclusions: applications to stochastic programming and mean field games
- A generalized forward-backward splitting operator: degenerate analysis and applications
- Convergence of the forward-backward algorithm: beyond the worst-case with the help of geometry
- Primal-dual splittings as fixed point iterations in the range of linear operators
- A primal-dual splitting algorithm for composite monotone inclusions with minimal lifting
- Hard-constrained inconsistent signal feasibility problems
- A UNIFIED FRAMEWORK FOR SOME INEXACT PROXIMAL POINT ALGORITHMS*
- A Class of Randomized Primal-Dual Algorithms for Distributed Optimization
- The Resolvent Average of Monotone Operators: Dominant and Recessive Properties
- Best Approximation from the Kuhn-Tucker Set of Composite Monotone Inclusions
- Preconditioning of a Generalized Forward-Backward Splitting and Application to Optimization on Graphs
- Stadium Norm and Douglas-Rachford Splitting: A New Approach to Road Design Optimization
- Splitting Methods in Communication, Imaging, Science, and Engineering
- Origin and Evolution of the Secant Method in One Dimension
- A Generalized Forward-Backward Splitting
- Optimal Transport with Proximal Splitting
- Proximal Splitting Methods in Signal Processing
- Convergence Analysis of Primal-Dual Algorithms for a Saddle-Point Problem: From Contraction Perspective
- Variational Analysis in Sobolev and BV Spaces
- Asynchronous Stochastic Coordinate Descent: Parallelism and Convergence Properties
- A survey on operator splitting and decomposition of convex programs
- On Weak Convergence of the Douglas–Rachford Method
- Tensor completion and low-n-rank tensor recovery via convex optimization
- A Dual Approach to Linear Inverse Problems with Convex Constraints
- A Parallel Splitting Method for Coupled Monotone Inclusions
- Inpainting by Flexible Haar-Wavelet Shrinkage
- A Monotone+Skew Splitting Model for Composite Monotone Inclusions in Duality
- The Numerical Solution of Parabolic and Elliptic Differential Equations
- On the Numerical Integration of $\frac{\partial ^2 u}{\partial x^2 } + \frac{\partial ^2 u}{\partial y^2 } = \frac{\partial u}{\partial t}$ by Implicit Methods
- On the Numerical Solution of Heat Conduction Problems in Two and Three Space Variables
- Proximity Maps for Convex Sets
- Dissipative Operators and Hyperbolic Systems of Partial Differential Equations
- Implicit Alternating Direction Methods
- Monotone networks
- The Cutting-Plane Method for Solving Convex Programs
- An Algorithm for Restricted Least Squares Regression
- Nonlinear Ill-posed Problems of Monotone Type
- Accelerating Block-Decomposition First-Order Methods for Solving Composite Saddle-Point and Two-Player Nash Equilibrium Problems
- Self-dual Partial Differential Systems and Their Variational Principles
- An EM algorithm for wavelet-based image restoration
- General Projective Splitting Methods for Sums of Maximal Monotone Operators
- Characterizing arbitrarily slow convergence in the method of alternating projections
- Convex Variational Formulation with Smooth Coupling for Multicomponent Signal Decomposition and Recovery
- Decomposition through formalization in a product space
- Applications of the method of partial inverses to convex programming: Decomposition
- Signal synthesis in the presence of an inconsistent set of constraints
- On Fixed Points of Non-Expansive Piecewise Isometric Mappings
- A Technique for the Numerical Solution of Certain Integral Equations of the First Kind
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