A Use of Conjugate Gradient Direction for the Convex Optimization Problem over the Fixed Point Set of a Nonexpansive Mapping
From MaRDI portal
Publication:3648534
DOI10.1137/070702497zbMath1176.47064OpenAlexW2067313264MaRDI QIDQ3648534
Publication date: 27 November 2009
Published in: SIAM Journal on Optimization (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/070702497
fixed pointnonexpansive mappingconvex optimization problemhybrid steepest descent methodconjugate gradient direction
Convex programming (90C25) Nonlinear programming (90C30) Variational and other types of inequalities involving nonlinear operators (general) (47J20) Numerical optimization and variational techniques (65K10) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Methods of reduced gradient type (90C52) Applications of operator theory in numerical analysis (47N40)
Related Items
Two algorithms for solving single-valued variational inequalities and fixed point problems ⋮ New iterative algorithms with self-adaptive step size for solving split equality fixed point problem and its applications ⋮ A strong convergence theorem for a general split equality problem with applications to optimization and equilibrium problem ⋮ A self-adaptive parallel subgradient extragradient method for finite family of pseudomonotone equilibrium and fixed point problems ⋮ Approximate solutions to variational inequality over the fixed point set of a strongly nonexpansive mapping ⋮ Acceleration of the Halpern algorithm to search for a fixed point of a nonexpansive mapping ⋮ Parallel computing subgradient method for nonsmooth convex optimization over the intersection of fixed point sets of nonexpansive mappings ⋮ Strong convergence of a self-adaptive inertial Tseng's extragradient method for pseudomonotone variational inequalities and fixed point problems ⋮ An extended projected residual algorithm for solving smooth convex optimization problems ⋮ Convergence analysis of iterative methods for nonsmooth convex optimization over fixed point sets of quasi-nonexpansive mappings ⋮ ITERATIVE COMPUTATION FOR SOLVING CONVEX OPTIMIZATION PROBLEMS OVER THE SET OF COMMON FIXED POINTS OF QUASI-NONEXPANSIVE AND DEMICONTRACTIVE MAPPINGS ⋮ Iterative algorithms for monotone variational inequality and fixed point problems on Hadamard manifolds ⋮ General algorithm for equilibrium problems and set-valued operators ⋮ Split equality monotone variational inclusions and fixed point problem of set-valued operator ⋮ Strong convergence of relaxed hybrid steepest-descent methods for triple hierarchical constrained optimization ⋮ Multistep hybrid extragradient method for triple hierarchical variational inequalities ⋮ A hierarchical variational inequality problem for generalized demimetric mappings with applications ⋮ Multi-step hybrid viscosity method for systems of variational inequalities defined over sets of solutions of an equilibrium problem and fixed point problems ⋮ Halpern subgradient extragradient method extended to equilibrium problems ⋮ Extragradient-proximal methods for split equilibrium and fixed point problems in Hilbert spaces ⋮ A general alternative regularization method with line search technique for solving split equilibrium and fixed point problems in Hilbert spaces ⋮ Hierarchical variational inequality problem and split common fixed point of averaged operators ⋮ A projected subgradient algorithm for bilevel equilibrium problems and applications ⋮ A unified implicit algorithm for solving the triple-hierarchical constrained optimization problem ⋮ A strong convergence theorem for solving pseudo-monotone variational inequalities using projection methods ⋮ Extragradient methods and linesearch algorithms for solving Ky Fan inequalities and fixed point problems ⋮ Unnamed Item ⋮ Some iterative methods for solving equilibrium problems and optimization problems ⋮ Algorithms for zeros of two accretive operators for solving convex minimization problems and its application to image restoration problems ⋮ A dynamic distributed conjugate gradient method for variational inequality problem over the common fixed-point constraints ⋮ Strong convergence for an iterative method for the triple-hierarchical constrained optimization problem ⋮ Fixed point optimization algorithm and its application to network bandwidth allocation ⋮ Three-term conjugate gradient method for the convex optimization problem over the fixed point set of a nonexpansive mapping ⋮ Fixed point optimization algorithm and its application to power control in CDMA data networks ⋮ A self-adaptive inertial subgradient extragradient method for pseudomonotone equilibrium and common fixed point problems ⋮ A new method for solving variational inequalities and fixed points problems of demi-contractive mappings in Hilbert spaces ⋮ Almost sure convergence of random projected proximal and subgradient algorithms for distributed nonsmooth convex optimization ⋮ Unnamed Item ⋮ Split equality problem with equilibrium problem, variational inequality problem, and fixed point problem of nonexpansive semigroups ⋮ Decentralized algorithm for centralized variational inequalities in network resource allocation ⋮ Iterative methods for triple hierarchical variational inequalities in Hilbert spaces ⋮ Inertial subgradient extragradient algorithms with line-search process for solving variational inequality problems and fixed point problems ⋮ A new generalized shrinkage conjugate gradient method for sparse recovery ⋮ Extrapolated sequential constraint method for variational inequality over the intersection of fixed-point sets ⋮ Mann-type algorithms for variational inequality problems and fixed point problems ⋮ Inertial extragradient method via viscosity approximation approach for solving equilibrium problem in Hilbert space ⋮ Approximating a common solution of extended split equality equilibrium and fixed point problems ⋮ Fejér-monotone hybrid steepest descent method for affinely constrained and composite convex minimization tasks ⋮ Projected viscosity subgradient methods for variational inequalities with equilibrium problem constraints in Hilbert spaces ⋮ Conjugate gradient methods using value of objective function for unconstrained optimization ⋮ General iterative algorithm for nonexpansive semigroups and variational inequalities in Hilbert spaces ⋮ Iterative algorithm for solving triple-hierarchical constrained optimization problem ⋮ Convex optimization over fixed point sets of quasi-nonexpansive and nonexpansive mappings in utility-based bandwidth allocation problems with operational constraints ⋮ New iterative scheme with strict pseudo-contractions and multivalued nonexpansive mappings for fixed point problems and variational inequality problems ⋮ Acceleration method for convex optimization over the fixed point set of a nonexpansive mapping ⋮ Convergence theorem for system of pseudomonotone equilibrium and split common fixed point problems in Hilbert spaces ⋮ Optimization for Inconsistent Split Feasibility Problems ⋮ Hybrid conjugate gradient method for a convex optimization problem over the fixed-point set of a nonexpansive mapping ⋮ Decentralized hierarchical constrained convex optimization ⋮ Strong convergence theorems for relatively nonexpansive mappings and Lipschitz-continuous monotone mappings in Banach spaces ⋮ Variational inequality over the set of common solutions of a system of bilevel variational inequality problem with applications ⋮ Extragradient subgradient methods for solving bilevel equilibrium problems ⋮ Bilevel Optimization as a Regularization Approach to Pseudomonotone Equilibrium Problems ⋮ On extragradient-viscosity methods for solving equilibrium and fixed point problems in a Hilbert space ⋮ Incremental subgradient method for nonsmooth convex optimization with fixed point constraints ⋮ Strong convergence of an inertial projection and contraction method with self adaptive stepsize for pseudomonotone variational inequalities and fixed point problems ⋮ Synchronal algorithm and cyclic algorithm for hierarchical fixed point problems and variational inequalities ⋮ Convergence analysis for variational inequalities and fixed point problems in reflexive Banach spaces ⋮ A self-adaptive Tseng extragradient method for solving monotone variational inequality and fixed point problems in Banach spaces ⋮ Bregman subgradient extragradient method with monotone self-adjustment stepsize for solving pseudo-monotone variational inequalities and fixed point problems ⋮ Relaxed hybrid steepest-descent methods with variable parameters for triple-hierarchical variational inequalities
Uses Software
