Mathematical programming, ISSN 1436-4646, 2011, Volume 137, Issue 1-2, pp. 91 - 129

In view of the minimization of a nonsmooth nonconvex function f, we prove an abstract convergence result for descent methods satisfying a sufficient-decrease...

Tame optimization | 65K15 | Theoretical, Mathematical and Computational Physics | Alternating minimization | Mathematics | Forward–backward splitting | Descent methods | 90C53 | Mathematical Methods in Physics | Iterative thresholding | Calculus of Variations and Optimal Control; Optimization | Proximal algorithms | Sufficient decrease | Combinatorics | 47J25 | Kurdyka–Łojasiewicz inequality | o-minimal structures | Nonconvex nonsmooth optimization | 34G25 | Semi-algebraic optimization | 47J30 | Mathematics of Computing | 90C25 | Numerical Analysis | Block-coordinate methods | Relative error | 49M15 | 49M37 | 47J35 | Kurdyka-Łojasiewicz inequality | Forward-backward splitting | MATHEMATICS, APPLIED | Kurdyka-Lojasiewicz inequality | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZATION | POINT ALGORITHM | Methods | Algorithms | Studies | Algebra | Analysis | Data smoothing | Optimization | Mathematical programming | Splitting | Gauss-Seidel method | Mathematical analysis | Minimization | Descent | Convergence

Tame optimization | 65K15 | Theoretical, Mathematical and Computational Physics | Alternating minimization | Mathematics | Forward–backward splitting | Descent methods | 90C53 | Mathematical Methods in Physics | Iterative thresholding | Calculus of Variations and Optimal Control; Optimization | Proximal algorithms | Sufficient decrease | Combinatorics | 47J25 | Kurdyka–Łojasiewicz inequality | o-minimal structures | Nonconvex nonsmooth optimization | 34G25 | Semi-algebraic optimization | 47J30 | Mathematics of Computing | 90C25 | Numerical Analysis | Block-coordinate methods | Relative error | 49M15 | 49M37 | 47J35 | Kurdyka-Łojasiewicz inequality | Forward-backward splitting | MATHEMATICS, APPLIED | Kurdyka-Lojasiewicz inequality | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZATION | POINT ALGORITHM | Methods | Algorithms | Studies | Algebra | Analysis | Data smoothing | Optimization | Mathematical programming | Splitting | Gauss-Seidel method | Mathematical analysis | Minimization | Descent | Convergence

Journal Article

Computational optimization and applications, ISSN 1573-2894, 2016, Volume 66, Issue 1, pp. 75 - 96

In this paper we propose several modified hybrid projection methods for solving common solutions to variational inequality problems involving monotone and...

65K15 | 68W10 | Mathematics | Statistics, general | 65Y05 | Optimization | Generalized equilibrium problem | 47H10 | Equilibrium problem | Variational inequality | Convex and Discrete Geometry | Operations Research, Management Science | Operation Research/Decision Theory | Extragradient method | 47H05 | Gradient method | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | EQUATIONS | MONOTONE MAPPINGS | ALGORITHMS | MIXED EQUILIBRIUM PROBLEMS | STRONG-CONVERGENCE THEOREM | EXTRAGRADIENT METHODS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | CYCLIC MONOTONICITY | HILBERT-SPACE | OPERATORS | Methods | Algorithms | Equality | Studies | Equilibrium | Operators | Computation | Inequalities | Projection | Mathematical models | Standards | Convergence

65K15 | 68W10 | Mathematics | Statistics, general | 65Y05 | Optimization | Generalized equilibrium problem | 47H10 | Equilibrium problem | Variational inequality | Convex and Discrete Geometry | Operations Research, Management Science | Operation Research/Decision Theory | Extragradient method | 47H05 | Gradient method | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | EQUATIONS | MONOTONE MAPPINGS | ALGORITHMS | MIXED EQUILIBRIUM PROBLEMS | STRONG-CONVERGENCE THEOREM | EXTRAGRADIENT METHODS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | CYCLIC MONOTONICITY | HILBERT-SPACE | OPERATORS | Methods | Algorithms | Equality | Studies | Equilibrium | Operators | Computation | Inequalities | Projection | Mathematical models | Standards | Convergence

Journal Article

Numerical algorithms, ISSN 1572-9265, 2017, Volume 78, Issue 4, pp. 1045 - 1060

In this paper, we study the weak and strong convergence of two algorithms for solving Lipschitz continuous and monotone variational inequalities. The...

65K15 | Numeric Computing | 68W10 | Variational inequality problem | Theory of Computation | Monotone operator | 65Y05 | Tseng’s extragradient method | Subgradient extragradient method | 47H10 | Algorithms | Algebra | Numerical Analysis | Viscosity method | Computer Science | Extragradient method | 47H05 | MATHEMATICS, APPLIED | Tseng's extragradient method | PROJECTION METHODS | EXTRAGRADIENT METHODS | BANACH-SPACES | MAPPINGS | ITERATIVE METHODS | VISCOSITY APPROXIMATION METHODS | HILBERT-SPACE | Analysis | Equality

65K15 | Numeric Computing | 68W10 | Variational inequality problem | Theory of Computation | Monotone operator | 65Y05 | Tseng’s extragradient method | Subgradient extragradient method | 47H10 | Algorithms | Algebra | Numerical Analysis | Viscosity method | Computer Science | Extragradient method | 47H05 | MATHEMATICS, APPLIED | Tseng's extragradient method | PROJECTION METHODS | EXTRAGRADIENT METHODS | BANACH-SPACES | MAPPINGS | ITERATIVE METHODS | VISCOSITY APPROXIMATION METHODS | HILBERT-SPACE | Analysis | Equality

Journal Article

Mathematical programming, ISSN 1436-4646, 2016, Volume 165, Issue 1, pp. 331 - 360

Variational inequality modeling, analysis and computations are important for many applications, but much of the subject has been developed in a deterministic...

65K15 | Theoretical, Mathematical and Computational Physics | Nonanticipativity | Price of information | Stochastic variational inequalities | Mathematics | Stochastic decomposition | 90C15 | Dualization | Mathematical Methods in Physics | Response rules | Multistage stochastic optimization | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | Multistage stochastic equilibrium | 49M27 | Combinatorics | MATHEMATICS, APPLIED | RESIDUAL MINIMIZATION METHOD | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | OPTIMIZATION | Decision-making | Analysis | Multistage | Equilibrium | Optimization | Inequalities | Mathematical programming

65K15 | Theoretical, Mathematical and Computational Physics | Nonanticipativity | Price of information | Stochastic variational inequalities | Mathematics | Stochastic decomposition | 90C15 | Dualization | Mathematical Methods in Physics | Response rules | Multistage stochastic optimization | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | Multistage stochastic equilibrium | 49M27 | Combinatorics | MATHEMATICS, APPLIED | RESIDUAL MINIMIZATION METHOD | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | OPTIMIZATION | Decision-making | Analysis | Multistage | Equilibrium | Optimization | Inequalities | Mathematical programming

Journal Article

Journal of global optimization, ISSN 1573-2916, 2017, Volume 70, Issue 2, pp. 385 - 399

The paper considers two extragradient-like algorithms for solving variational inequality problems involving strongly pseudomonotone and Lipschitz continuous...

65K15 | Pseudomonotone operator | Strongly pseudomonotone operator | 68W10 | Variational inequality problem | Mathematics | Monotone operator | Strongly monotone operator | 65Y05 | Optimization | Subgradient extragradient method | Projection method | 47H10 | Operations Research/Decision Theory | Extragradient method | Computer Science, general | 47H05 | Real Functions | MATHEMATICS, APPLIED | EQUATIONS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | BANACH-SPACES | MAPPINGS | SYSTEMS | HILBERT-SPACE | Algorithms | Mathematical analysis | Hilbert space

65K15 | Pseudomonotone operator | Strongly pseudomonotone operator | 68W10 | Variational inequality problem | Mathematics | Monotone operator | Strongly monotone operator | 65Y05 | Optimization | Subgradient extragradient method | Projection method | 47H10 | Operations Research/Decision Theory | Extragradient method | Computer Science, general | 47H05 | Real Functions | MATHEMATICS, APPLIED | EQUATIONS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | BANACH-SPACES | MAPPINGS | SYSTEMS | HILBERT-SPACE | Algorithms | Mathematical analysis | Hilbert space

Journal Article

Mathematical programming, ISSN 1436-4646, 2019, Volume 176, Issue 1-2, pp. 497 - 544

This paper considers nonconvex distributed constrained optimization over networks, modeled as directed (possibly time-varying) graphs. We introduce the first...

65K15 | Theoretical, Mathematical and Computational Physics | Mathematics | Mathematical Methods in Physics | 91A10 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | 90C33 | 90C90 | 65K10 | 49M27 | Combinatorics | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Analysis | Algorithms | Machine learning | Economic models | Mathematical models | Graph theory | Nonlinear programming | Engineering education | Optimization | Convergence

65K15 | Theoretical, Mathematical and Computational Physics | Mathematics | Mathematical Methods in Physics | 91A10 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | 90C33 | 90C90 | 65K10 | 49M27 | Combinatorics | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Analysis | Algorithms | Machine learning | Economic models | Mathematical models | Graph theory | Nonlinear programming | Engineering education | Optimization | Convergence

Journal Article

Numerische Mathematik, ISSN 0029-599X, 05/2018, Volume 139, Issue 1, pp. 27 - 45

Journal Article

Mathematical programming, ISSN 1436-4646, 2018, Volume 177, Issue 1-2, pp. 255 - 289

In this paper, we propose a discretization scheme for the two-stage stochastic linear complementarity problem (LCP) where the underlying random data are...

Ex post equilibrium | 65K15 | Theoretical, Mathematical and Computational Physics | Error bound | Mathematics | 90C15 | Two-stage stochastic linear complementarity problem | Mathematical Methods in Physics | Distributionally robust linear complementarity problem | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | 90C33 | Combinatorics | Discrete approximation | VARIATIONAL-INEQUALITIES | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | PROGRAMS | BOUNDS | CONVERGENCE | Analysis | Hedging (Finance) | Discretization | Game theory | Qualitative analysis

Ex post equilibrium | 65K15 | Theoretical, Mathematical and Computational Physics | Error bound | Mathematics | 90C15 | Two-stage stochastic linear complementarity problem | Mathematical Methods in Physics | Distributionally robust linear complementarity problem | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | 90C33 | Combinatorics | Discrete approximation | VARIATIONAL-INEQUALITIES | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | PROGRAMS | BOUNDS | CONVERGENCE | Analysis | Hedging (Finance) | Discretization | Game theory | Qualitative analysis

Journal Article

Numerische Mathematik, ISSN 0029-599X, 5/2018, Volume 139, Issue 1, pp. 27 - 45

This paper is concerned with a priori error estimates for the piecewise linear finite element approximation of the classical obstacle problem. We demonstrate...

65N15 | Mathematical Methods in Physics | 65K15 | Numerical Analysis | Theoretical, Mathematical and Computational Physics | Mathematical and Computational Engineering | Mathematics, general | Mathematics | Numerical and Computational Physics, Simulation | 65N30

65N15 | Mathematical Methods in Physics | 65K15 | Numerical Analysis | Theoretical, Mathematical and Computational Physics | Mathematical and Computational Engineering | Mathematics, general | Mathematics | Numerical and Computational Physics, Simulation | 65N30

Journal Article

Calcolo, ISSN 1126-5434, 2015, Volume 53, Issue 2, pp. 189 - 199

In this paper, a general accelerated modulus-based matrix splitting iteration method is established, which covers the known general modulus-based matrix...

65K15 | Modulus-based method | Numerical Analysis | Mathematics | Theory of Computation | Linear complementarity problem | Convergence | MATHEMATICS | MULTISPLITTING METHODS | Texts | Splitting | Mathematical models | Central processing units | Iterative methods

65K15 | Modulus-based method | Numerical Analysis | Mathematics | Theory of Computation | Linear complementarity problem | Convergence | MATHEMATICS | MULTISPLITTING METHODS | Texts | Splitting | Mathematical models | Central processing units | Iterative methods

Journal Article

Mathematical programming, ISSN 1436-4646, 2018, Volume 177, Issue 1-2, pp. 225 - 253

In this paper, we present a method for identifying infeasible, unbounded, and pathological conic programs based on Douglas–Rachford splitting. When an...

65K15 | 65K05 | Theoretical, Mathematical and Computational Physics | Douglas–Rachford splitting | Mathematics | Unbounded | Mathematical Methods in Physics | Conic programs | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90C25 | Numerical Analysis | Pathological | Infeasible | Combinatorics | 47H05 | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Douglas-Rachford splitting | FACIAL REDUCTION | OPTIMIZATION | SUM | ALGORITHMS | Usage | Algorithms | Splitting | Subroutines | Optimization | Hyperplanes

65K15 | 65K05 | Theoretical, Mathematical and Computational Physics | Douglas–Rachford splitting | Mathematics | Unbounded | Mathematical Methods in Physics | Conic programs | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90C25 | Numerical Analysis | Pathological | Infeasible | Combinatorics | 47H05 | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Douglas-Rachford splitting | FACIAL REDUCTION | OPTIMIZATION | SUM | ALGORITHMS | Usage | Algorithms | Splitting | Subroutines | Optimization | Hyperplanes

Journal Article

Numerische Mathematik, ISSN 0945-3245, 2014, Volume 130, Issue 4, pp. 579 - 613

We develop a novel convergence theory for the multilevel sample variance estimators in the framework of the multilevel Monte Carlo methods. We prove that,...

Mathematical Methods in Physics | 65K15 | 65C30 | Numerical Analysis | Theoretical, Mathematical and Computational Physics | Appl.Mathematics/Computational Methods of Engineering | Numerical and Computational Physics | Mathematics, general | Mathematics | 65C05 | 65N55 | 65N30 | EQUATIONS | MATHEMATICS, APPLIED | ELLIPTIC VARIATIONAL-INEQUALITIES | MULTIGRID METHODS | Monte Carlo method

Mathematical Methods in Physics | 65K15 | 65C30 | Numerical Analysis | Theoretical, Mathematical and Computational Physics | Appl.Mathematics/Computational Methods of Engineering | Numerical and Computational Physics | Mathematics, general | Mathematics | 65C05 | 65N55 | 65N30 | EQUATIONS | MATHEMATICS, APPLIED | ELLIPTIC VARIATIONAL-INEQUALITIES | MULTIGRID METHODS | Monte Carlo method

Journal Article

Mathematical Programming, ISSN 0025-5610, 5/2019, Volume 175, Issue 1, pp. 241 - 262

We study the convergence of an inexact version of the classical Krasnosel’skii–Mann iteration for computing fixed points of nonexpansive maps. Our main result...

60J10 | 65J08 | 65K15 | Theoretical, Mathematical and Computational Physics | Mathematics | Mathematical Methods in Physics | 47H10 | Fixed point iterations | Evolution equations | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Rates of convergence | Numerical Analysis | 47H09 | Combinatorics | Nonexpansive maps | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Iterative methods | Banach space | Convergence

60J10 | 65J08 | 65K15 | Theoretical, Mathematical and Computational Physics | Mathematics | Mathematical Methods in Physics | 47H10 | Fixed point iterations | Evolution equations | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Rates of convergence | Numerical Analysis | 47H09 | Combinatorics | Nonexpansive maps | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Iterative methods | Banach space | Convergence

Journal Article

Computational optimization and applications, ISSN 1573-2894, 2015, Volume 63, Issue 1, pp. 143 - 168

In this paper, we consider the tensor generalized eigenvalue complementarity problem (TGEiCP), which is an interesting generalization of matrix eigenvalue...

Eigenvalue complementarity problem | 65K15 | Optimization reformulation | Cone eigenvalue | Projection algorithm | Mathematics | Statistics, general | 15A69 | Optimization | 15A18 | 90C30 | Convex and Discrete Geometry | 90C33 | Operations Research, Management Science | Operation Research/Decision Theory | Higher order tensor | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | PERRON-FROBENIUS THEOREM | Algorithms | Computer science | Studies | Analysis | Eigen values | Tensors | Upper bounds | Computation | Mathematical analysis | Eigenvalues | Projection

Eigenvalue complementarity problem | 65K15 | Optimization reformulation | Cone eigenvalue | Projection algorithm | Mathematics | Statistics, general | 15A69 | Optimization | 15A18 | 90C30 | Convex and Discrete Geometry | 90C33 | Operations Research, Management Science | Operation Research/Decision Theory | Higher order tensor | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | PERRON-FROBENIUS THEOREM | Algorithms | Computer science | Studies | Analysis | Eigen values | Tensors | Upper bounds | Computation | Mathematical analysis | Eigenvalues | Projection

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2018, Volume 2018, Issue 1, pp. 1 - 13

The Schwarz algorithm for a class of elliptic quasi-variational inequalities with nonlinear source terms is studied in this work. The authors prove a new error...

65N15 | 65K15 | Mathematics | Schwarz algorithm | Quasi-variational inequalities | Error estimates | Overlapping grids | Analysis | Mathematics, general | Applications of Mathematics | Stability property | 65N30 | 05C38 | MATHEMATICS | MATHEMATICS, APPLIED | APPROXIMATION | Research

65N15 | 65K15 | Mathematics | Schwarz algorithm | Quasi-variational inequalities | Error estimates | Overlapping grids | Analysis | Mathematics, general | Applications of Mathematics | Stability property | 65N30 | 05C38 | MATHEMATICS | MATHEMATICS, APPLIED | APPROXIMATION | Research

Journal Article

Journal of optimization theory and applications, ISSN 1573-2878, 2018, Volume 178, Issue 1, pp. 219 - 239

In this paper, we study the variational inequalities involving monotone and Lipschitz continuous mapping in Banach spaces. A new and simple iterative method,...

Strong convergence | 65K15 | Variational inequality problem | Mathematics | Theory of Computation | Optimization | Subgradient extragradient method | 47J20 | Line-search | Calculus of Variations and Optimal Control; Optimization | 90C25 | Operations Research/Decision Theory | Halpern method | Applications of Mathematics | Engineering, general | 47H05 | 47J25 | COMMON SOLUTIONS | MATHEMATICS, APPLIED | SMOOTHNESS | EQUATIONS | CONVEX-SETS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MAPPINGS | HILBERT-SPACE | OPERATORS | FIXED-POINTS | STRONG-CONVERGENCE | Analysis | Methods | Algorithms | Error analysis | Inequalities | Hilbert space | Banach spaces | Iterative methods | Banach space | Convergence

Strong convergence | 65K15 | Variational inequality problem | Mathematics | Theory of Computation | Optimization | Subgradient extragradient method | 47J20 | Line-search | Calculus of Variations and Optimal Control; Optimization | 90C25 | Operations Research/Decision Theory | Halpern method | Applications of Mathematics | Engineering, general | 47H05 | 47J25 | COMMON SOLUTIONS | MATHEMATICS, APPLIED | SMOOTHNESS | EQUATIONS | CONVEX-SETS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MAPPINGS | HILBERT-SPACE | OPERATORS | FIXED-POINTS | STRONG-CONVERGENCE | Analysis | Methods | Algorithms | Error analysis | Inequalities | Hilbert space | Banach spaces | Iterative methods | Banach space | Convergence

Journal Article

Demonstratio mathematica, ISSN 2391-4661, 2018, Volume 51, Issue 1, pp. 211 - 232

The purpose of this paper is to study a split generalized mixed equilibrium problem and a fixed point problem for nonspreading mappings in real Hilbert...

65K15 | 90C33 | viscosity approximation method | iterative method | 47J25 | fixed point problem | accelerated algorithm | 65J15 | split mixed equilibrium | nonspreading mapping

65K15 | 90C33 | viscosity approximation method | iterative method | 47J25 | fixed point problem | accelerated algorithm | 65J15 | split mixed equilibrium | nonspreading mapping

Journal Article

Numerical algorithms, ISSN 1572-9265, 2017, Volume 78, Issue 3, pp. 827 - 845

In this paper, we introduce the modified proximal point algorithm for common fixed points of asymptotically quasi-nonexpansive mappings in CAT(0) spaces and...

65K15 | Convex minimization problem | Numeric Computing | Theory of Computation | Proximal point algorithm | CAT spaces | Asymptotically quasi-nonexpansive mapping | 47H10 | Algorithms | Algebra | Common fixed point | Numerical Analysis | Computer Science | 47H09 | 65K10 | MATHEMATICS, APPLIED | HARMONIC MAPS | METRIC-SPACES | GEODESIC SPACES | THEOREMS | HADAMARD MANIFOLDS | Medical colleges | Analysis | Resveratrol

65K15 | Convex minimization problem | Numeric Computing | Theory of Computation | Proximal point algorithm | CAT spaces | Asymptotically quasi-nonexpansive mapping | 47H10 | Algorithms | Algebra | Common fixed point | Numerical Analysis | Computer Science | 47H09 | 65K10 | MATHEMATICS, APPLIED | HARMONIC MAPS | METRIC-SPACES | GEODESIC SPACES | THEOREMS | HADAMARD MANIFOLDS | Medical colleges | Analysis | Resveratrol

Journal Article