Journal of optimization theory and applications, ISSN 1573-2878, 2018, Volume 179, Issue 3, pp. 838 - 867

We examine a class of stochastic mirror descent dynamics in the context of monotone variational inequalities (including Nash equilibrium and saddle-point...

Stochastic differential equations | 2 International | EQUATIONS | ALGORITHMS | 6 Data source | Mirror descent | 90C25 | 90C47 | LONG-TIME BEHAVIOR | 90C33 | SYSTEMS | FLOWS | Saddle-point problems | OPERATORS | Variational inequalities | Mathematics | Theory of Computation | Optimization | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Applications of Mathematics | Engineering, general | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Game theory | Business schools | Differential equations | Dynamic tests | Sequences | Parameters | Saddle points | Inequalities | Brownian movements | Descent | Convergence | Optimization and Control

Stochastic differential equations | 2 International | EQUATIONS | ALGORITHMS | 6 Data source | Mirror descent | 90C25 | 90C47 | LONG-TIME BEHAVIOR | 90C33 | SYSTEMS | FLOWS | Saddle-point problems | OPERATORS | Variational inequalities | Mathematics | Theory of Computation | Optimization | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Applications of Mathematics | Engineering, general | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Game theory | Business schools | Differential equations | Dynamic tests | Sequences | Parameters | Saddle points | Inequalities | Brownian movements | Descent | Convergence | Optimization and Control

Journal Article

Journal of the Australian Mathematical Society (2001), ISSN 1446-8107, 2019, pp. 1 - 23

As a continuation of previous work of the first author with Ranjbar [â€˜A variational inequality in complete CAT(0) spacesâ€™, (2015), 557â€“574] on a special form...

secondary 90C25 | 47J20 | primary 47H05 | 49J40 | 2010 Mathematics subject classification | 65K10 | 47J25

secondary 90C25 | 47J20 | primary 47H05 | 49J40 | 2010 Mathematics subject classification | 65K10 | 47J25

Journal Article

Mathematical programming, ISSN 1436-4646, 2012, Volume 141, Issue 1-2, pp. 349 - 382

We present in this paper alternating linearization algorithms based on an alternating direction augmented Lagrangian approach for minimizing the sum of two...

Alternating direction method | Primary 65K05 | Augmented Lagrangian method | Optimal gradient method | Variable splitting | Gauss-Seidel method | Theoretical, Mathematical and Computational Physics | Mathematics | Alternating linearization method | Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Convex optimization | 90C25 | Numerical Analysis | Peaceman-Rachford method | Secondary 68Q25 | Combinatorics | MATHEMATICS, APPLIED | DECOMPOSITION | MODEL | INVERSE | COMPUTER SCIENCE, SOFTWARE ENGINEERING | RECOVERY | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | SPLITTING ALGORITHM | SELECTION | Methods | Management science | Algorithms | Studies | Splitting | Computation | Mathematical analysis | Mathematical models | Iterative methods | Optimization | Linearization

Alternating direction method | Primary 65K05 | Augmented Lagrangian method | Optimal gradient method | Variable splitting | Gauss-Seidel method | Theoretical, Mathematical and Computational Physics | Mathematics | Alternating linearization method | Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Convex optimization | 90C25 | Numerical Analysis | Peaceman-Rachford method | Secondary 68Q25 | Combinatorics | MATHEMATICS, APPLIED | DECOMPOSITION | MODEL | INVERSE | COMPUTER SCIENCE, SOFTWARE ENGINEERING | RECOVERY | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | SPLITTING ALGORITHM | SELECTION | Methods | Management science | Algorithms | Studies | Splitting | Computation | Mathematical analysis | Mathematical models | Iterative methods | Optimization | Linearization

Journal Article

Mathematical Programming Computation, ISSN 1867-2949, 9/2019, Volume 11, Issue 3, pp. 503 - 586

We introduce Sieve-SDP, a simple facial reduction algorithm to preprocess semidefinite programs (SDPs). Sieve-SDP inspects the constraints of the problem to...

Strong duality | Semidefinite programming | Preprocessing | 90-08 | Strict feasibility | 90C06 | Mathematics | Theory of Computation | Optimization | Facial reduction | Polynomial optimization | Mathematics of Computing | 90C25 | Operations Research/Decision Theory | 90C22 | Mathematics - Optimization and Control

Strong duality | Semidefinite programming | Preprocessing | 90-08 | Strict feasibility | 90C06 | Mathematics | Theory of Computation | Optimization | Facial reduction | Polynomial optimization | Mathematics of Computing | 90C25 | Operations Research/Decision Theory | 90C22 | Mathematics - Optimization and Control

Journal Article

Foundations of computational mathematics, ISSN 1615-3383, 2015, Volume 16, Issue 4, pp. 1031 - 1068

Many problems can be formulated as recovering a low-rank tensor. Although an increasingly common task, tensor recovery remains a challenging problem because of...

Secondary 90C59 | Subdifferential | Linear and Multilinear Algebras, Matrix Theory | Mathematics | Primary 90C25 | Tensor completion | 15A52 | Nuclear norm minimization | Tensor rank | Convex optimization | Numerical Analysis | Dual certificate | Concentration inequality | Applications of Mathematics | Math Applications in Computer Science | Computer Science, general | Economics, general | Matrix completion | MATHEMATICS | MATHEMATICS, APPLIED | COMPUTER SCIENCE, THEORY & METHODS | Analysis | Tensors (Mathematics) | Tensors | Convexity | Mathematical analysis | Martingales | Algebra | Matrices (mathematics) | Norms | Minimization | Optimization

Secondary 90C59 | Subdifferential | Linear and Multilinear Algebras, Matrix Theory | Mathematics | Primary 90C25 | Tensor completion | 15A52 | Nuclear norm minimization | Tensor rank | Convex optimization | Numerical Analysis | Dual certificate | Concentration inequality | Applications of Mathematics | Math Applications in Computer Science | Computer Science, general | Economics, general | Matrix completion | MATHEMATICS | MATHEMATICS, APPLIED | COMPUTER SCIENCE, THEORY & METHODS | Analysis | Tensors (Mathematics) | Tensors | Convexity | Mathematical analysis | Martingales | Algebra | Matrices (mathematics) | Norms | Minimization | Optimization

Journal Article

Annals of Statistics, ISSN 0090-5364, 02/2019, Volume 47, Issue 1, pp. 127 - 155

We introduce a new approach aiming at computing approximate optimal designs for multivariate polynomial regressions on compact (semialgebraic) design spaces....

Equivalence theorem | Semidefinite programming | Christoffel polynomial | Experimental design | Linear model | semidefinite programming | STATISTICS & PROBABILITY | linear model | equivalence theorem | Statistics | Mathematics | Optimization and Control

Equivalence theorem | Semidefinite programming | Christoffel polynomial | Experimental design | Linear model | semidefinite programming | STATISTICS & PROBABILITY | linear model | equivalence theorem | Statistics | Mathematics | Optimization and Control

Journal Article

Journal of mathematical analysis and applications, ISSN 0022-247X, 2015, Volume 421, Issue 1, pp. 1 - 20

We introduce regularity notions for averaged nonexpansive operators. Combined with regularity notions of their fixed point sets, we obtain linear and strong...

Douglasâ€“Rachford algorithm | Averaged nonexpansive mapping | Projection | Nonexpansive operator | Convex feasibility problem | Bounded linear regularity | Douglas-Rachford algorithm | MATHEMATICS | MATHEMATICS, APPLIED | REGULARITY | PROJECTIONS | Analysis | Algorithms

Douglasâ€“Rachford algorithm | Averaged nonexpansive mapping | Projection | Nonexpansive operator | Convex feasibility problem | Bounded linear regularity | Douglas-Rachford algorithm | MATHEMATICS | MATHEMATICS, APPLIED | REGULARITY | PROJECTIONS | Analysis | Algorithms

Journal Article

Mathematical programming, ISSN 1436-4646, 2014, Volume 152, Issue 1-2, pp. 405 - 434

We propose a novel distributed method for convex optimization problems with a certain separability structure. The method is based on the augmented Lagrangian...

Alternating direction method | Secondary 49M27 | Theoretical, Mathematical and Computational Physics | Network optimization | Monotropic programming | Mathematics | Primary 90C25 | 90C15 | Diagonal quadratic approximation | Stochastic programming | Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Convex optimization | Numerical Analysis | Combinatorics | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | DECOMPOSITION METHOD | Studies | Lagrange multiplier | Mathematical models | Convex analysis | Mathematical programming | Networks | Mathematical analysis | Decomposition | Stochasticity | Optimization | Convergence

Alternating direction method | Secondary 49M27 | Theoretical, Mathematical and Computational Physics | Network optimization | Monotropic programming | Mathematics | Primary 90C25 | 90C15 | Diagonal quadratic approximation | Stochastic programming | Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Convex optimization | Numerical Analysis | Combinatorics | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | DECOMPOSITION METHOD | Studies | Lagrange multiplier | Mathematical models | Convex analysis | Mathematical programming | Networks | Mathematical analysis | Decomposition | Stochasticity | Optimization | Convergence

Journal Article

Mathematical programming, ISSN 1436-4646, 2018, Volume 178, Issue 1-2, pp. 503 - 558

We consider global efficiency of algorithms for minimizing a sum of a convex function and a composition of a Lipschitz convex function with a smooth map. The...

Secondary 90C06 | Fast gradient methods | Inexactness | Theoretical, Mathematical and Computational Physics | Mathematics | Gaussâ€“Newton | Complexity | Prox-gradient | Mathematical Methods in Physics | Incremental methods | Primary 97N60 | 90C30 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Composite minimization | Smoothing | 90C25 | Numerical Analysis | Combinatorics | Acceleration | REGRESSION | MATHEMATICS, APPLIED | ALGORITHM | LEAST-SQUARES | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZATION | CONVERGENCE | Gauss-Newton | Algorithms | Composition | Maps | Convexity | Efficiency

Secondary 90C06 | Fast gradient methods | Inexactness | Theoretical, Mathematical and Computational Physics | Mathematics | Gaussâ€“Newton | Complexity | Prox-gradient | Mathematical Methods in Physics | Incremental methods | Primary 97N60 | 90C30 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Composite minimization | Smoothing | 90C25 | Numerical Analysis | Combinatorics | Acceleration | REGRESSION | MATHEMATICS, APPLIED | ALGORITHM | LEAST-SQUARES | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZATION | CONVERGENCE | Gauss-Newton | Algorithms | Composition | Maps | Convexity | Efficiency

Journal Article

Journal of optimization theory and applications, ISSN 1573-2878, 2019, Volume 183, Issue 1, pp. 179 - 198

The Douglasâ€“Rachford method is a popular splitting technique for finding a zero of the sum of two subdifferential operators of proper, closed, and convex...

Lipschitz continuous mapping | Secondary 49M29 | Mathematics | Theory of Computation | Strongly monotone operator | Optimization | Strongly convex function | Skew-symmetric operator | Linear convergence | Primary 47H05 | Calculus of Variations and Optimal Control; Optimization | 90C25 | Operations Research/Decision Theory | Douglasâ€“Rachford algorithm | 47H09 | 49M27 | 49N15 | Applications of Mathematics | Engineering, general | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Douglas-Rachford algorithm | INCLUSIONS | ALGORITHMS | Electrical engineering | Algorithms | Operators (mathematics) | Splitting | Convergence

Lipschitz continuous mapping | Secondary 49M29 | Mathematics | Theory of Computation | Strongly monotone operator | Optimization | Strongly convex function | Skew-symmetric operator | Linear convergence | Primary 47H05 | Calculus of Variations and Optimal Control; Optimization | 90C25 | Operations Research/Decision Theory | Douglasâ€“Rachford algorithm | 47H09 | 49M27 | 49N15 | Applications of Mathematics | Engineering, general | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Douglas-Rachford algorithm | INCLUSIONS | ALGORITHMS | Electrical engineering | Algorithms | Operators (mathematics) | Splitting | Convergence

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 09/2016, Volume 504, pp. 406 - 432

During the last decade, the paradigm of compressed sensing has gained significant importance in the signal processing community. While the original idea was to...

Convex geometry | Sparse recovery | Grassmannian condition number | Compressed sensing | MATHEMATICS | MATHEMATICS, APPLIED | NUMBER | Signal processing | Algorithms | Mathematics - Functional Analysis

Convex geometry | Sparse recovery | Grassmannian condition number | Compressed sensing | MATHEMATICS | MATHEMATICS, APPLIED | NUMBER | Signal processing | Algorithms | Mathematics - Functional Analysis

Journal Article

SIAM Journal on Optimization, ISSN 1052-6234, 2017, Volume 27, Issue 4, pp. 2356 - 2380

Fixed point iterations play a central role in the design and the analysis of a large number of optimization algorithms. We study a new iterative scheme in...

Proximal algorithm | Fixed point iteration | Monotone operator splitting | Nonsmooth minimization | Averaged operator | Mean value iterations | Forward-backward algorithm | Inertial algorithm | Peacemanâ€“Rachford algorithm | SYSTEM | MATHEMATICS, APPLIED | forward-backward algorithm | MAXIMAL MONOTONE-OPERATORS | fixed point iteration | monotone operator splitting | mean value iterations | FIXED-POINT ITERATIONS | Peaceman-Rachford algorithm | nonsmooth minimization | averaged operator | proximal algorithm | CONVERGENCE | inertial algorithm | Mathematics

Proximal algorithm | Fixed point iteration | Monotone operator splitting | Nonsmooth minimization | Averaged operator | Mean value iterations | Forward-backward algorithm | Inertial algorithm | Peacemanâ€“Rachford algorithm | SYSTEM | MATHEMATICS, APPLIED | forward-backward algorithm | MAXIMAL MONOTONE-OPERATORS | fixed point iteration | monotone operator splitting | mean value iterations | FIXED-POINT ITERATIONS | Peaceman-Rachford algorithm | nonsmooth minimization | averaged operator | proximal algorithm | CONVERGENCE | inertial algorithm | Mathematics

Journal Article

Mathematical Programming, ISSN 0025-5610, 3/2018, Volume 168, Issue 1, pp. 55 - 61

The problem of finding a zero of the sum of two maximally monotone operators is of central importance in optimization. One successful method to find such a...

Theoretical, Mathematical and Computational Physics | Primary 47H09 | Proximal mapping | Mathematics | Nowhere dense set | Maximally monotone operator | Mathematical Methods in Physics | Resolvent | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90C25 | Numerical Analysis | Firmly nonexpansive mapping | Douglasâ€“Rachford algorithm | Combinatorics | Secondary 47H05 | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Douglas-Rachford algorithm | POINT ALGORITHM | Algorithms | Operators | Mapping

Theoretical, Mathematical and Computational Physics | Primary 47H09 | Proximal mapping | Mathematics | Nowhere dense set | Maximally monotone operator | Mathematical Methods in Physics | Resolvent | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90C25 | Numerical Analysis | Firmly nonexpansive mapping | Douglasâ€“Rachford algorithm | Combinatorics | Secondary 47H05 | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Douglas-Rachford algorithm | POINT ALGORITHM | Algorithms | Operators | Mapping

Journal Article

Foundations of Computational Mathematics, ISSN 1615-3375, 12/2019, Volume 19, Issue 6, pp. 1265 - 1313

In this paper, we investigate the sample size requirement for exact recovery of a high-order tensor of low rank from a subset of its entries. We show that a...

Secondary 90C59 | Nonconvex optimization | Linear and Multilinear Algebras, Matrix Theory | Mathematics | Primary 90C25 | Polynomial time complexity | Tensor completion | 15A52 | Tensor rank | Numerical Analysis | U-statistics | Concentration inequality | Applications of Mathematics | Math Applications in Computer Science | Computer Science, general | Economics, general | Matrix completion | Polynomials | Research | Mathematical research | Tensors (Mathematics) | Data processing | Tensors | Algorithms | Mathematical analysis | Spectral methods

Secondary 90C59 | Nonconvex optimization | Linear and Multilinear Algebras, Matrix Theory | Mathematics | Primary 90C25 | Polynomial time complexity | Tensor completion | 15A52 | Tensor rank | Numerical Analysis | U-statistics | Concentration inequality | Applications of Mathematics | Math Applications in Computer Science | Computer Science, general | Economics, general | Matrix completion | Polynomials | Research | Mathematical research | Tensors (Mathematics) | Data processing | Tensors | Algorithms | Mathematical analysis | Spectral methods

Journal Article

Mathematical Programming, ISSN 0025-5610, 9/2016, Volume 159, Issue 1, pp. 109 - 136

This paper studies several classes of nonconvex optimization problems defined over convex cones, establishing connections between them and demonstrating that...

Completely positive representation | Theoretical, Mathematical and Computational Physics | Mathematics | 90C26 | Local optimality | Conic QPCC | Mathematical Methods in Physics | 90C46 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90C25 | Numerical Analysis | 90C11 | 90C22 | 90C33 | Primary 90C20 | Conic QCQP | Rank-constrained SDP | Secondary 65K05 | Combinatorics | EXISTENCE | MATHEMATICS, APPLIED | LINEAR COMPLEMENTARITY CONSTRAINTS | OPTIMIZATION PROBLEMS | APPROXIMATION | DECOMPOSITION | SEMIDEFINITE | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | RELAXATIONS | CONSTRAINED QUADRATIC PROGRAMS | MATHEMATICAL PROGRAMS | NONCONVEX | Conics | Constraints | Equivalence | Paper | Texts | Feasibility | Joints | Optimization

Completely positive representation | Theoretical, Mathematical and Computational Physics | Mathematics | 90C26 | Local optimality | Conic QPCC | Mathematical Methods in Physics | 90C46 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90C25 | Numerical Analysis | 90C11 | 90C22 | 90C33 | Primary 90C20 | Conic QCQP | Rank-constrained SDP | Secondary 65K05 | Combinatorics | EXISTENCE | MATHEMATICS, APPLIED | LINEAR COMPLEMENTARITY CONSTRAINTS | OPTIMIZATION PROBLEMS | APPROXIMATION | DECOMPOSITION | SEMIDEFINITE | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | RELAXATIONS | CONSTRAINED QUADRATIC PROGRAMS | MATHEMATICAL PROGRAMS | NONCONVEX | Conics | Constraints | Equivalence | Paper | Texts | Feasibility | Joints | Optimization

Journal Article

Numerical Algorithms, ISSN 1017-1398, 9/2016, Volume 73, Issue 1, pp. 33 - 76

We systematically study the optimal linear convergence rates for several relaxed alternating projection methods and the generalized Douglas-Rachford splitting...

Principal angle | Generalized Douglas-Rachford method | Secondary 65F15, 65B05, 15A18, 90C25, 41A25 | Numeric Computing | Theory of Computation | Friedrichs angle | Convergent and semi-convergent matrix | Relaxed alternating projection method | Linear convergence | Algorithms | Algebra | Numerical Analysis | Primary 65F10, 65K05 | Computer Science | CONVEX FEASIBILITY PROBLEMS | MATHEMATICS, APPLIED | ALGORITHMS | ANGLES | SYSTEMS | ITERATIVE METHODS | SINGULAR MATRICES | OPERATORS | Matrices (mathematics) | Mathematical analysis | Eigenvalues | Projection | Subspaces | Matrix methods | Optimization | Convergence

Principal angle | Generalized Douglas-Rachford method | Secondary 65F15, 65B05, 15A18, 90C25, 41A25 | Numeric Computing | Theory of Computation | Friedrichs angle | Convergent and semi-convergent matrix | Relaxed alternating projection method | Linear convergence | Algorithms | Algebra | Numerical Analysis | Primary 65F10, 65K05 | Computer Science | CONVEX FEASIBILITY PROBLEMS | MATHEMATICS, APPLIED | ALGORITHMS | ANGLES | SYSTEMS | ITERATIVE METHODS | SINGULAR MATRICES | OPERATORS | Matrices (mathematics) | Mathematical analysis | Eigenvalues | Projection | Subspaces | Matrix methods | Optimization | Convergence

Journal Article

Mathematical Programming, ISSN 0025-5610, 7/2016, Volume 158, Issue 1, pp. 1 - 21

This paper presents an algorithm for approximately minimizing a convex function in simple, not necessarily bounded convex, finite-dimensional domains, assuming...

68Q25 | 65K05 | Strongly convex | Theoretical, Mathematical and Computational Physics | Nesterovâ€™s optimal method | Mathematics | Primary 90C25 | Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Convex optimization | Numerical Analysis | Complexity bound | Large-scale optimization | Nonsmooth optimization | 49M37 | Combinatorics | Secondary 90C60 | Optimal subgradient method | Optimal first-order method | Smooth optimization | MATHEMATICS, APPLIED | GRADIENT METHODS | CONVEX-OPTIMIZATION | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZATION | SCALE | Nesterov's optimal method | Algorithms | Studies | Mathematical models | Convex analysis | Mathematical programming

68Q25 | 65K05 | Strongly convex | Theoretical, Mathematical and Computational Physics | Nesterovâ€™s optimal method | Mathematics | Primary 90C25 | Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Convex optimization | Numerical Analysis | Complexity bound | Large-scale optimization | Nonsmooth optimization | 49M37 | Combinatorics | Secondary 90C60 | Optimal subgradient method | Optimal first-order method | Smooth optimization | MATHEMATICS, APPLIED | GRADIENT METHODS | CONVEX-OPTIMIZATION | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZATION | SCALE | Nesterov's optimal method | Algorithms | Studies | Mathematical models | Convex analysis | Mathematical programming

Journal Article

Numerical functional analysis and optimization, ISSN 1532-2467, 2005, Volume 25, Issue 7-8, pp. 619 - 655

The hybrid steepest descent method is an algorithmic solution to the variational inequality problem over the fixed point set of nonlinear mapping and...

Quasi-nonexpansive mapping | Primary 47H10, 90C25 | Secondary 47H09, 90C30 | Hybrid steepest descent method | Variational inequality problem | Fixed point | Inverse problem | inverse problem | CONVEX FEASIBILITY PROBLEMS | MATHEMATICS, APPLIED | IMAGE-RESTORATION | APPROXIMATION | hybrid steepest descent method | ALGORITHMS | CONSTRAINT | MINIMIZATION | fixed point | CONVERGENCE | HILBERT-SPACE | REGULARIZATION | PROJECTIONS | variational inequality problem | quasi-nonexpansive mapping

Quasi-nonexpansive mapping | Primary 47H10, 90C25 | Secondary 47H09, 90C30 | Hybrid steepest descent method | Variational inequality problem | Fixed point | Inverse problem | inverse problem | CONVEX FEASIBILITY PROBLEMS | MATHEMATICS, APPLIED | IMAGE-RESTORATION | APPROXIMATION | hybrid steepest descent method | ALGORITHMS | CONSTRAINT | MINIMIZATION | fixed point | CONVERGENCE | HILBERT-SPACE | REGULARIZATION | PROJECTIONS | variational inequality problem | quasi-nonexpansive mapping

Journal Article