Forcing strong convergence of proximal point iterations in a Hilbert space
From MaRDI portal
Publication:1970303
DOI10.1007/s101079900113zbMath0971.90062OpenAlexW1495915592MaRDI QIDQ1970303
Mikhail V. Solodov, Benar Fux Svaiter
Publication date: 31 July 2000
Published in: Mathematical Programming. Series A. Series B (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s101079900113
Numerical mathematical programming methods (65K05) Convex programming (90C25) Applications of functional analysis in optimization, convex analysis, mathematical programming, economics (46N10)
Related Items
A new self-adaptive CQ algorithm with an application to the LASSO problem ⋮ Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups. ⋮ An explicit iteration for zeros of accretive operators ⋮ Convergence theorems for maximal monotone operators and fixed point problems in Banach spaces ⋮ Error sensitivity for strongly convergent modifications of the proximal point algorithm ⋮ Approximation of a zero point of monotone operators with nonsummable errors ⋮ Strong convergence theorems by hybrid methods for the split common null point problem in Banach spaces ⋮ Strong convergence theorems for the general split variational inclusion problem in Hilbert spaces ⋮ A new hybrid algorithm and its numerical realization for two nonexpansive mappings ⋮ Generalized proximal-type methods for weak vector variational inequality problems in Banach spaces ⋮ Hybrid iterative algorithms for two families of finite maximal monotone mappings ⋮ Non-convex hybrid algorithm for a family of countable quasi-Lipschitz mappings and application ⋮ Cyclic subgradient extragradient methods for equilibrium problems ⋮ Regularization methods for nonexpansive semigroups in Hilbert spaces ⋮ A regularization method for the proximal point algorithm ⋮ A shrinking projection method for nonexpansive mappings with nonsummable errors in a Hadamard space ⋮ Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces ⋮ Regularization proximal point algorithm for finding a common fixed point of a finite family of nonexpansive mappings in Banach spaces ⋮ Modified extragradient method for variational inequalities and verification of solution existence ⋮ The viscosity approximation forward-backward splitting method for zeros of the sum of monotone operators ⋮ Strong convergence in Hilbert spaces via \(\varGamma \)-duality ⋮ Proximal point algorithms for finding a zero of a finite sum of monotone mappings in Banach spaces ⋮ Convergence of a hybrid iterative method for finite families of generalized quasi-\(\phi\)-asymptotically nonexpansive mappings ⋮ Hybrid approximate proximal method with auxiliary variational inequality for vector optimization ⋮ Hybrid proximal point algorithm and applications to equilibrium problems and convex programming ⋮ Convergence results for the zero-finding problem and fixed points of nonexpansive semigroups and strict pseudocontractions ⋮ A hybrid approximation method for equilibrium, variational inequality and fixed point problems ⋮ Simple projection algorithm for a countable family of weak relatively nonexpansive mappings and applications ⋮ Strong convergence of a proximal-type algorithm for an occasionally pseudomonotone operator in Banach spaces ⋮ About the relaxed cocoercivity and the convergence of the proximal point algorithm ⋮ Iterative methods for a class of variational inequalities in Hilbert spaces ⋮ Realization of the hybrid method for Mann iterations ⋮ Parallel iterative methods for Bregman strongly nonexpansive operators in reflexive Banach spaces ⋮ Strong convergence theorems for the split variational inclusion problem in Hilbert spaces ⋮ A regularization algorithm for zero points of accretive operators ⋮ An approximate proximal point algorithm for maximal monotone inclusion problems ⋮ Hybrid proximal-type algorithms for generalized equilibrium problems, maximal monotone operators, and relatively nonexpansive mappings ⋮ Strong convergence theorems for 2-generalized hybrid mappings in Hilbert spaces ⋮ Regularization proximal point algorithm for common fixed points of nonexpansive mappings in Banach spaces ⋮ Strong convergence theorems for zeros of bounded maximal monotone nonlinear operators ⋮ Shrinking projection methods for firmly nonexpansive mappings ⋮ New monotone hybrid algorithm for hemi-relatively nonexpansive mappings and maximal monotone operators ⋮ Hybrid Mann-Halpern iteration methods for nonexpansive mappings and semigroups ⋮ Interior proximal methods for quasiconvex optimization ⋮ Strong convergence of an iterative scheme by a new type of projection method for a family of quasinonexpansive mappings ⋮ Approximating fixed points of infinite nonexpansive mappings by the hybrid method ⋮ A proximal point based approach to optimal control of affine switched systems ⋮ Convergence theorems based on the shrinking projection method for hemi-relatively nonexpansive mappings, variational inequalities and equilibrium problems ⋮ Hybrid shrinking projection method for a generalized equilibrium problem, a maximal monotone operator and a countable family of relatively nonexpansive mappings ⋮ Hybrid Ishikawa iterative methods for a nonexpansive semigroup in Hilbert space ⋮ Averaged mappings and the gradient-projection algorithm ⋮ Strong convergence theorems for variational inequality problems and quasi-\(\phi\)-asymptotically nonexpansive mappings ⋮ Approximations for nonlinear mappings by the hybrid method in Hilbert spaces ⋮ Approximating common solution of variational inequality problems for two monotone mappings in Banach spaces ⋮ Viscosity approximations by the shrinking projection method in Hilbert spaces ⋮ A strongly convergent hybrid proximal method in Banach spaces. ⋮ A subgradient-like algorithm for solving vector convex inequalities ⋮ A strong convergence algorithm for the two-operator split common fixed point problem in Hilbert spaces ⋮ General split variational inclusion problem in Hilbert spaces ⋮ Strong convergence studied by a hybrid type method for monotone operators in a Banach space ⋮ On convergence criteria of generalized proximal point algorithms ⋮ General proximal-point algorithm for monotone operators ⋮ Strong convergence for gradient projection method and relatively nonexpansive mappings in Banach spaces ⋮ A hybrid method without extrapolation step for solving variational inequality problems ⋮ Modified proximal-point algorithm for maximal monotone operators in Banach spaces ⋮ Iterative schemes for zero points of maximal monotone operators and fixed points of nonexpansive mappings and their applications ⋮ A strongly convergent shrinking descent-like Halpern's method for monotone variational inequality and fixed point problems ⋮ A new multi-step iterative algorithm for approximating common fixed points of a finite family of multi-valued Bregman relatively nonexpansive mappings ⋮ A generalized inexact proximal point method for nonsmooth functions that satisfies Kurdyka Łojasiewicz inequality ⋮ Iterative methods for zeros of a monotone variational inclusion in Hilbert spaces ⋮ Solving variational inequalities involving nonexpansive type mappings ⋮ Proximal primal-dual best approximation algorithm with memory ⋮ A subgradient extragradient algorithm for solving multi-valued variational inequality ⋮ Strong convergence of a splitting proximal projection method for the sum of two maximal monotone operators ⋮ Strong convergence of generalized projection algorithms for nonlinear operators ⋮ Approximate generalized proximal-type method for convex vector optimization problem in Banach spaces ⋮ A note on the regularized proximal point algorithm ⋮ Strong convergence theorem for nonexpansive semigroups in Hilbert space ⋮ Weak and strong convergence theorems for maximal monotone operators in a Banach space ⋮ A strong convergence theorem for relatively nonexpansive mappings in a Banach space ⋮ Strong convergence theorem of an iterative method for variational inequalities and fixed point problems in Hilbert spaces ⋮ Existence of fixed points of firmly nonexpansive-like mappings in Banach spaces ⋮ Strong convergence theorems obtained by a generalized projections hybrid method for families of mappings in Banach spaces ⋮ Asymptotic analysis for proximal-type methods in vector variational inequality problems ⋮ Line search fixed point algorithms based on nonlinear conjugate gradient directions: application to constrained smooth convex optimization ⋮ Strong convergence theorems for monotone mappings and relatively weak nonexpansive mappings ⋮ On strong convergence by the hybrid method for families of mappings in Hilbert spaces ⋮ Equivalent theorems of the convergence between proximal type algorithms ⋮ Strong convergence of projection scheme for zeros of maximal monotone operators ⋮ Strong convergence theorems by the hybrid method for families of mappings in Banach spaces ⋮ A new hybrid iterative method for solution of equilibrium problems and fixed point problems for an inverse strongly monotone operator and a nonexpansive mapping ⋮ Iterative convergence theorems for maximal monotone operators and relatively nonexpansive mappings ⋮ Strong convergence of monotone hybrid method for maximal monotone operators and hemirelatively nonexpansive mappings ⋮ Super-relaxed \((\eta)\)-proximal point algorithms, relaxed \((\eta)\)-proximal point algorithms, linear convergence analysis, and nonlinear variational inclusions ⋮ Two projection algorithms for solving the split common fixed point problem ⋮ On the strong convergence of the proximal point algorithm with an application to Hammerstein euations ⋮ A shrinking projection algorithm with errors for Costerro bounded linear mappings ⋮ A variant of the hybrid proximal extragradient method for solving strongly monotone inclusions and its complexity analysis ⋮ Iterative algorithms with errors for zeros of accretive operators in Banach spaces ⋮ Weak convergence of a hybrid type method with errors for a maximal monotone mapping in Banach spaces ⋮ Parallel iterative methods for solving systems of generalized mixed equilibrium problems in reflexive Banach spaces ⋮ An explicit algorithm for monotone variational inequalities ⋮ Approximate proximal methods in vector optimization ⋮ Iterative methods for strict pseudo-contractions in Hilbert spaces ⋮ Regularization of proximal point algorithms in Hadamard manifolds ⋮ Strong convergence theorems for strict pseudo-contractions in Hilbert spaces ⋮ Strong and weak convergence of the modified proximal point algorithms in Hilbert space ⋮ On two iterative methods for mixed monotone variational inequalities ⋮ A Strong Convergence Theorem by the Shrinking Projection Method for the Split Common Null Point Problem in Banach Spaces ⋮ Forcing strong convergence of Korpelevich's method in Banach spaces with its applications in game theory ⋮ Parallel and cyclic hybrid subgradient extragradient methods for variational inequalities ⋮ Strong convergence analysis of common variational inclusion problems involving an inertial parallel monotone hybrid method for a novel application to image restoration ⋮ A projection algorithm for non-monotone variational inequalities ⋮ The split common null point problem for generalized resolvents in two Banach spaces ⋮ New inertial method for generalized split variational inclusion problems ⋮ On the contraction-proximal point algorithms with multi-parameters ⋮ General-type proximal point algorithm for solving inclusion and fixed point problems with composite operators ⋮ On a proximal-point algorithm for solving the minimization problem and common fixed-point problem in CAT\((k)\) spaces ⋮ Two modified proximal point algorithms in geodesic spaces with curvature bounded above ⋮ Hybrid algorithm of fixed point for weak relatively nonexpansive multivalued mappings and applications ⋮ Resolvent and proximal compositions ⋮ Adaptive inertial subgradient extragradient methods for finding minimum-norm solutions of pseudomonotone variational inequalities ⋮ Convergence Rate of Inexact Proximal Point Algorithms for Operator with Hölder Metric Subregularity ⋮ On the weak and strong convergence of modified forward-backward-half-forward splitting methods ⋮ Weak and strong convergence of generalized proximal point algorithms with relaxed parameters ⋮ Proximal Point Method for Quasi-Equilibrium Problems in Banach Spaces ⋮ Strong convergence by the shrinking effect of two half-spaces and applications ⋮ Composite iterative schemes for maximal monotone operators in reflexive Banach spaces ⋮ Hybrid extragradient iterative algorithms for variational inequalities, variational inclusions, and fixed-point problems ⋮ The split common fixed point problem for generalized demimetric mappings in two Banach spaces ⋮ Modified proximal point algorithms involving convex combination technique for solving minimization problems with convergence analysis ⋮ Unnamed Item ⋮ Accelerated hybrid and shrinking projection methods for variational inequality problems ⋮ Strong convergence of a splitting projection method for the sum of maximal monotone operators ⋮ STRONG CONVERGENCE OF SOME ALGORITHMS FOR λ-STRICT PSEUDO-CONTRACTIONS IN HILBERT SPACE ⋮ A new iterative method based on the modified proximal-point algorithm for finding a common null point of an infinite family of accretive operators in Banach spaces ⋮ Generalized proximal point algorithms for multiobjective optimization problems ⋮ An inexact proximal-type algorithm in Banach spaces ⋮ A family of projective splitting methods for the sum of two maximal monotone operators ⋮ Strong Convergence of a Projection-Type Method for Mixed Variational Inequalities in Hilbert Spaces ⋮ An inexact proximal-type method for the generalized variational inequality in Banach spaces ⋮ Iterative algorithm for approximating solutions of maximal monotone operators in Hilbert spaces ⋮ New hybrid projection methods for variational inequalities involving pseudomonotone mappings ⋮ A New Algorithm for Solving The Multiple-Sets Split Feasibility Problem in Banach Spaces ⋮ Parallel iterative methods for a finite family of sequences of nearly nonexpansive mappings in Hilbert spaces ⋮ The contraction-proximal point algorithm with square-summable errors ⋮ A new proximal point iteration that converges weakly but not in norm ⋮ Approximating common fixed points of averaged self-mappings with applications to the split feasibility problem and maximal monotone operators in Hilbert spaces ⋮ Convergence of the modified Mann's iteration method for asymptotically strict pseudo-contractions ⋮ Projective splitting methods for sums of maximal monotone operators with applications ⋮ Strong convergence of extragradient method for generalized variational inequalities in Hilbert space ⋮ Hybrid shrinking iterative solutions to convex feasibility problems for countable families of relatively nonexpansive mappings and a system of generalized mixed equilibrium problems ⋮ Strong convergence of a splitting algorithm for treating monotone operators ⋮ Approximation of zeros of bounded maximal monotone mappings, solutions of Hammerstein integral equations and convex minimization problems ⋮ Strong convergence of the CQ method for fixed point iteration processes ⋮ Unnamed Item ⋮ Regularization inertial proximal point algorithm for common solutions of a finite family of inverse-strongly monotone equations ⋮ Convergence analysis of inexact proximal point algorithms on Hadamard manifolds ⋮ Strong Convergence Theorems for a Finite Family of Sequences of Nearly Nonexpansive Mappings in Hilbert Spaces ⋮ Quantitative results on a Halpern-type proximal point algorithm ⋮ Construction of best Bregman approximations in reflexive Banach spaces ⋮ Best Approximation from the Kuhn-Tucker Set of Composite Monotone Inclusions ⋮ Hybrid Mann-Halpern iteration methods for finding fixed points involving asymptotically nonexpansive mappings and semigroups ⋮ Unnamed Item ⋮ Strong convergence of an inertial algorithm for maximal monotone inclusions with applications ⋮ Iterative algorithm for zeros of multivalued accretive operators in certain Banach spaces ⋮ On Weak and Strong Convergence of the Projected Gradient Method for Convex Optimization in Real Hilbert Spaces ⋮ Viscosity approximation methods for countable families of nonexpansive mappings in Banach spaces ⋮ Unnamed Item ⋮ Metastability of the proximal point algorithm with multi-parameters ⋮ An algorithm for computing zeros of generalized phi-strongly monotone and bounded maps in classical Banach spaces ⋮ A strongly convergent proximal point method for vector optimization ⋮ Unnamed Item ⋮ A Strong Convergence Theorem for an Iterative Method for Finding Zeros of Maximal Monotone Maps with Applications to Convex Minimization and Variational Inequality Problems ⋮ Unnamed Item ⋮ New strong convergence method for the sum of two maximal monotone operators ⋮ On convergence of the proximal point algorithm in Banach spaces ⋮ A unified iterative treatment for solutions of problems of split feasibility and equilibrium in Hilbert spaces ⋮ A projection-type method for multivalued variational inequality ⋮ Algorithms for nonexpansive self-mappings with application to the constrained multiple-set split convex feasibility fixed point problem in Hilbert spaces ⋮ An iterative Bregman regularization method for optimal control problems with inequality constraints ⋮ Convergence results of forward-backward algorithms for sum of monotone operators in Banach spaces ⋮ A Strongly Convergent Method for Nonsmooth Convex Minimization in Hilbert Spaces ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Strong convergence to a solution of a variational inequality problem in Banach spaces ⋮ Two strong convergence theorems for the common null point problem in Banach spaces ⋮ Unnamed Item ⋮ The split common null point problem in Banach spaces ⋮ Image restoration by advanced parallel inertial forward-backward splitting methods ⋮ Strong convergent iterative techniques for 2-generalized hybrid mappings and split equilibrium problems ⋮ Strong convergence of Halpern iteration for products of finitely many resolvents of maximal monotone operators in Banach spaces
