Advances in Computational Mathematics, ISSN 1019-7168, 4/2013, Volume 38, Issue 3, pp. 667 - 681

We consider the problem of solving dual monotone inclusions involving sums of composite parallel-sum type operators. A feature of this work is to exploit...

Monotone inclusion | Primal-dual algorithm | Cocoercivity | Numeric Computing | Theory of Computation | Duality | Monotone operator | Forward-backward algorithm | Algebra | Calculus of Variations and Optimal Control; Optimization | 90C25 | Computer Science | Composite operator | Operator splitting | 49M29 | Mathematics, general | 49M27 | 47H05 | MATHEMATICS, APPLIED | DECOMPOSITION | CONVEX MINIMIZATION PROBLEMS | VARIATIONAL-INEQUALITIES | CONVERGENCE | Duality theory (Mathematics) | Algorithms | Research | Monotonic functions | Operator theory | Operators | Splitting | Computation | Mathematical models | Inclusions | Sums

Monotone inclusion | Primal-dual algorithm | Cocoercivity | Numeric Computing | Theory of Computation | Duality | Monotone operator | Forward-backward algorithm | Algebra | Calculus of Variations and Optimal Control; Optimization | 90C25 | Computer Science | Composite operator | Operator splitting | 49M29 | Mathematics, general | 49M27 | 47H05 | MATHEMATICS, APPLIED | DECOMPOSITION | CONVEX MINIMIZATION PROBLEMS | VARIATIONAL-INEQUALITIES | CONVERGENCE | Duality theory (Mathematics) | Algorithms | Research | Monotonic functions | Operator theory | Operators | Splitting | Computation | Mathematical models | Inclusions | Sums

Journal Article

Mathematika, ISSN 0025-5793, 01/2014, Volume 60, Issue 1, pp. 101 - 107

Journal Article

Set-Valued and Variational Analysis, ISSN 1877-0533, 6/2012, Volume 20, Issue 2, pp. 307 - 330

We propose a primal-dual splitting algorithm for solving monotone inclusions involving a mixture of sums, linear compositions, and parallel sums of set-valued...

Monotone inclusion | Nonsmooth convex optimization | Mathematics | Maximal monotone operator | Geometry | 90C25 | Analysis | Splitting algorithm | 49M29 | 49M27 | 49N15 | Parallel sum | 47H05 | Set-valued duality | MATHEMATICS, APPLIED | STABILITY | DECOMPOSITION | PROXIMAL POINT ALGORITHM | VARIATIONAL-INEQUALITIES | RECOVERY | MINIMIZATION | MAPPINGS | Algorithms | Optimization and Control

Monotone inclusion | Nonsmooth convex optimization | Mathematics | Maximal monotone operator | Geometry | 90C25 | Analysis | Splitting algorithm | 49M29 | 49M27 | 49N15 | Parallel sum | 47H05 | Set-valued duality | MATHEMATICS, APPLIED | STABILITY | DECOMPOSITION | PROXIMAL POINT ALGORITHM | VARIATIONAL-INEQUALITIES | RECOVERY | MINIMIZATION | MAPPINGS | Algorithms | Optimization and Control

Journal Article

Arabian Journal of Mathematics, ISSN 2193-5343, 9/2016, Volume 5, Issue 3, pp. 159 - 175

In this paper, we introduce a cyclic subgradient extragradient algorithm and its modified form for finding a solution of a system of equilibrium problems for a...

Mathematics, general | Mathematics | 47H05 | 47J25 | 65J15 | 91B50

Mathematics, general | Mathematics | 47H05 | 47J25 | 65J15 | 91B50

Journal Article

Journal of the Australian Mathematical Society, ISSN 1446-7887, 2019, pp. 1 - 23

Journal Article

1998, Grundlehren der mathematischen Wissenschaften, ISBN 9783540627722, Volume 317, xiii, 733

Book

Optimization Methods and Software, ISSN 1055-6788, 2018, pp. 1 - 21

Journal Article

Applicable Analysis, ISSN 0003-6811, 10/2019, Volume 98, Issue 13, pp. 2423 - 2439

In this paper, we revisit the numerical approach to variational inequality problems involving strongly monotone and Lipschitz continuous operators by a variant...

strongly monotone operator | Projection method | Variational inequality | 47H05 | 47J25 | 65J15 | 65Y05 | Lipschitz continuity | 91B50 | Operators | Algorithms | Convergence

strongly monotone operator | Projection method | Variational inequality | 47H05 | 47J25 | 65J15 | 65Y05 | Lipschitz continuity | 91B50 | Operators | Algorithms | Convergence

Journal Article

Archiv der Mathematik, ISSN 0003-889X, 8/2008, Volume 91, Issue 2, pp. 166 - 177

In this paper, the class of nonspreading mappings in Banach spaces is introduced. This class contains the recently introduced class of firmly nonexpansive type...

Firmly nonexpansive mapping | firmly nonexpansive type mapping | Mathematics, general | Mathematics | Secondary 47H05 | resolvent of monotone operator | Primary 47H10 | fixed point theorem | nonspreading mapping | Fixed point theorem | Nonspreading mapping | Firmly nonexpansive type mapping | Resolvent of monotone operator | firmly nonexpansive mapping | CONVERGENCE THEOREM | MATHEMATICS | DISTANCES | WEAK-CONVERGENCE | FIRMLY NONEXPANSIVE-MAPPINGS

Firmly nonexpansive mapping | firmly nonexpansive type mapping | Mathematics, general | Mathematics | Secondary 47H05 | resolvent of monotone operator | Primary 47H10 | fixed point theorem | nonspreading mapping | Fixed point theorem | Nonspreading mapping | Firmly nonexpansive type mapping | Resolvent of monotone operator | firmly nonexpansive mapping | CONVERGENCE THEOREM | MATHEMATICS | DISTANCES | WEAK-CONVERGENCE | FIRMLY NONEXPANSIVE-MAPPINGS

Journal Article

Computational Optimization and Applications, ISSN 0926-6003, 1/2017, 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

Advances in Nonlinear Analysis, ISSN 2191-9496, 02/2018, Volume 7, Issue 1, pp. 35 - 48

The paper is devoted to the Dirichlet problem for monotone, in general multivalued, elliptic equations with nonstandard growth condition. The growth conditions...

35R70 | 35J60 | multivalued monotone operator | Nonstandard growth condition | monotone elliptic equation | 35J25 | 47H05 | MATHEMATICS | MATHEMATICS, APPLIED | SOBOLEV SPACES | EQUATIONS | HOMOGENIZATION

35R70 | 35J60 | multivalued monotone operator | Nonstandard growth condition | monotone elliptic equation | 35J25 | 47H05 | MATHEMATICS | MATHEMATICS, APPLIED | SOBOLEV SPACES | EQUATIONS | HOMOGENIZATION

Journal Article

Journal of Optimization Theory and Applications, ISSN 0022-3239, 06/2019, Volume 181, Issue 3, pp. 709 - 726

The averaged alternating modified reflections algorithm is a projection method for finding the closest point in the intersection of closed and convex sets to a...

Maximally monotone operator | Douglas–Rachford algorithm | Resolvent | Splitting method | Averaged alternating modified reflections algorithm | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | 65K05 | Douglas-Rachford algorithm | 47H05 | 47J25 | 47N10 | Computational geometry | Operators | Splitting | Hilbert space | Algorithms | Convexity

Maximally monotone operator | Douglas–Rachford algorithm | Resolvent | Splitting method | Averaged alternating modified reflections algorithm | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | 65K05 | Douglas-Rachford algorithm | 47H05 | 47J25 | 47N10 | Computational geometry | Operators | Splitting | Hilbert space | Algorithms | Convexity

Journal Article

Journal of Optimization Theory and Applications, ISSN 0022-3239, 07/2019, Volume 182, Issue 1, pp. 110 - 132

The Alternating Minimization Algorithm has been proposed by Paul Tseng to solve convex programming problems with two-block separable linear constraints and...

Fenchel duality | Lagrangian | Convex optimization | Saddle points | Subdifferential | Proximal AMA | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Image processing | Algorithms | Machine learning | Operators (mathematics) | Computational geometry | Mathematical analysis | Hilbert space | Convexity | Iterative methods | Optimization | Mathematical programming | 65K05 | 90C25 | 47H05

Fenchel duality | Lagrangian | Convex optimization | Saddle points | Subdifferential | Proximal AMA | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Image processing | Algorithms | Machine learning | Operators (mathematics) | Computational geometry | Mathematical analysis | Hilbert space | Convexity | Iterative methods | Optimization | Mathematical programming | 65K05 | 90C25 | 47H05

Journal Article

Mathematische Nachrichten, ISSN 0025-584X, 10/2019, Volume 292, Issue 10, pp. 2108 - 2128

We consider strongly monotone continuous planar vector fields with a finite number of fixed points. The fixed points fall into three classes, attractors,...

47H10 | planar map | strongly monotone map | 47H05 | fixed point | winding number

47H10 | planar map | strongly monotone map | 47H05 | fixed point | winding number

Journal Article

Optimization, ISSN 0233-1934, 11/2019, Volume 68, Issue 11, pp. 2071 - 2087

In this paper, we deal with three aspects of p-cyclically monotone operators. First, we introduce a notion of monotone polar adapted for p-cyclically monotone...

linear p-cyclically monotone operators | Fitzpatrick functions of order p | 49J53 | Brézis-Browder theorem | p-cyclically monotone operators | 47H05 | 47H04 | Banach space | Linear operators

linear p-cyclically monotone operators | Fitzpatrick functions of order p | 49J53 | Brézis-Browder theorem | p-cyclically monotone operators | 47H05 | 47H04 | Banach space | Linear operators

Journal Article

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, ISSN 0022-3239, 06/2019, Volume 181, Issue 3, pp. 864 - 882

We consider the regularization of two proximal point algorithms (PPA) with errors for a maximal monotone operator in a real Hilbert space, previously studied,...

MATHEMATICS, APPLIED | 90C29 | Maximal monotone operator | Resolvent operator | Proximal point algorithm | ASYMPTOTIC-BEHAVIOR | Metric projection | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | 47H09 | 90C90 | Hilbert space | 47J25 | 47H05 | Theorems | Algorithms | Parameters | Error correction | Regularization | Optimization | Convergence

MATHEMATICS, APPLIED | 90C29 | Maximal monotone operator | Resolvent operator | Proximal point algorithm | ASYMPTOTIC-BEHAVIOR | Metric projection | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | 47H09 | 90C90 | Hilbert space | 47J25 | 47H05 | Theorems | Algorithms | Parameters | Error correction | Regularization | Optimization | Convergence

Journal Article

Journal of Global Optimization, ISSN 0925-5001, 6/2018, Volume 71, Issue 2, pp. 341 - 360

In this paper, first, we review the projection and contraction methods for solving the split feasibility problem (SFP), and then by using the inverse strongly...

CQ method | Mathematics | Split feasibility problem | Optimization | Projection and contraction method | 54H25 | 47H10 | Operations Research/Decision Theory | 47H07 | Computer Science, general | 47H05 | Real Functions | Modified projection and contraction method | Inverse strongly monotone | Projection | Convexity | Mathematical analysis | Feasibility studies

CQ method | Mathematics | Split feasibility problem | Optimization | Projection and contraction method | 54H25 | 47H10 | Operations Research/Decision Theory | 47H07 | Computer Science, general | 47H05 | Real Functions | Modified projection and contraction method | Inverse strongly monotone | Projection | Convexity | Mathematical analysis | Feasibility studies

Journal Article

Optimization, ISSN 0233-1934, 10/2019, Volume 68, Issue 10, pp. 1855 - 1880

We investigate a forward-backward splitting algorithm of penalty type with inertial effects for finding the zeros of the sum of a maximally monotone operator...

Maximally monotone operator | convex bilevel optimization | 65K05 | Fitzpatrick function | 90C25 | forward-backward splitting algorithm | 47H05 | forward–backward splitting algorithm | Operators (mathematics) | Algorithms | Inclusions | Convergence | Ergodic processes

Maximally monotone operator | convex bilevel optimization | 65K05 | Fitzpatrick function | 90C25 | forward-backward splitting algorithm | 47H05 | forward–backward splitting algorithm | Operators (mathematics) | Algorithms | Inclusions | Convergence | Ergodic processes

Journal Article

19.
Full Text
Asynchronous block-iterative primal-dual decomposition methods for monotone inclusions

Mathematical Programming, ISSN 0025-5610, 3/2018, Volume 168, Issue 1, pp. 645 - 672

We propose new primal-dual decomposition algorithms for solving systems of inclusions involving sums of linearly composed maximally monotone operators. The...

Monotone inclusion | Primal-dual algorithm | 65K05 | Theoretical, Mathematical and Computational Physics | Mathematics | Duality | Monotone operator | Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90C25 | Numerical Analysis | Splitting algorithm | 49M27 | Block-iterative algorithm | Combinatorics | Asynchronous algorithm | 47H05 | HILBERT-SPACES | MATHEMATICS, APPLIED | KUHN-TUCKER SET | ALGORITHMS | SUMS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | SYSTEMS | OPERATORS | PROJECTIVE SPLITTING METHODS | STRONG-CONVERGENCE | Methods | Algorithms | Half spaces | Innovations | Decomposition | Inclusions | Linear operators | Convergence

Monotone inclusion | Primal-dual algorithm | 65K05 | Theoretical, Mathematical and Computational Physics | Mathematics | Duality | Monotone operator | Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90C25 | Numerical Analysis | Splitting algorithm | 49M27 | Block-iterative algorithm | Combinatorics | Asynchronous algorithm | 47H05 | HILBERT-SPACES | MATHEMATICS, APPLIED | KUHN-TUCKER SET | ALGORITHMS | SUMS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | SYSTEMS | OPERATORS | PROJECTIVE SPLITTING METHODS | STRONG-CONVERGENCE | Methods | Algorithms | Half spaces | Innovations | Decomposition | Inclusions | Linear operators | Convergence

Journal Article

Numerical Algorithms, ISSN 1017-1398, 8/2018, 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

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