Journal of Global Optimization, ISSN 0925-5001, 11/2018, Volume 72, Issue 3, pp. 553 - 577

The proximal point algorithm is a widely used tool for solving a variety of convex optimization problems such as finding zeros of maximally monotone operators,...

Jointly firmly nonexpansive families | Uniformly firmly nonexpansive mappings | Mathematics | Proximal point algorithm | Optimization | CAT spaces | Convex optimization | Rates of convergence | 90C25 | Operations Research/Decision Theory | Proof mining | 47H09 | Computer Science, general | 47J25 | 46N10 | 03F10 | Real Functions | MATHEMATICS, APPLIED | HARMONIC MAPS | METRIC-SPACES | GEODESIC SPACES | ASYMPTOTIC-BEHAVIOR | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | VECTOR OPTIMIZATION | FUNCTIONAL-ANALYSIS | FIRMLY NONEXPANSIVE-MAPPINGS | LOGICAL METATHEOREMS | FIXED-POINTS | MONOTONE-OPERATORS | Computer science | Mineral industry | Algorithms | Numerical analysis | Mining industry | Analysis | Computational geometry | Fixed points (mathematics) | Hilbert space | Convexity | Data mining | Convex analysis | Convergence

Jointly firmly nonexpansive families | Uniformly firmly nonexpansive mappings | Mathematics | Proximal point algorithm | Optimization | CAT spaces | Convex optimization | Rates of convergence | 90C25 | Operations Research/Decision Theory | Proof mining | 47H09 | Computer Science, general | 47J25 | 46N10 | 03F10 | Real Functions | MATHEMATICS, APPLIED | HARMONIC MAPS | METRIC-SPACES | GEODESIC SPACES | ASYMPTOTIC-BEHAVIOR | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | VECTOR OPTIMIZATION | FUNCTIONAL-ANALYSIS | FIRMLY NONEXPANSIVE-MAPPINGS | LOGICAL METATHEOREMS | FIXED-POINTS | MONOTONE-OPERATORS | Computer science | Mineral industry | Algorithms | Numerical analysis | Mining industry | Analysis | Computational geometry | Fixed points (mathematics) | Hilbert space | Convexity | Data mining | Convex analysis | Convergence

Journal Article

Journal of Optimization Theory and Applications, ISSN 0022-3239, 9/2019, Volume 182, Issue 3, pp. 1120 - 1129

This note is a reaction to the recent paper by Rouhani and Moradi (J Optim Theory Appl 172:222–235, 2017), where a proximal point algorithm proposed by...

Strong convergence | Mathematics | Theory of Computation | Maximal monotone operator | Proximal point algorithm | Optimization | Calculus of Variations and Optimal Control; Optimization | 90C25 | Operations Research/Decision Theory | 90C90 | Convex function | Applications of Mathematics | Engineering, general | 47J25 | 47H05 | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | STRONG-CONVERGENCE | Algorithms | Hilbert space

Strong convergence | Mathematics | Theory of Computation | Maximal monotone operator | Proximal point algorithm | Optimization | Calculus of Variations and Optimal Control; Optimization | 90C25 | Operations Research/Decision Theory | 90C90 | Convex function | Applications of Mathematics | Engineering, general | 47J25 | 47H05 | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | STRONG-CONVERGENCE | Algorithms | Hilbert space

Journal Article

Journal of Optimization Theory and Applications, ISSN 0022-3239, 5/2014, Volume 161, Issue 2, pp. 478 - 489

In this paper, we consider the proximal point algorithm for the problem of finding zeros of any given maximal monotone operator in an infinite-dimensional...

Convex minimization | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Mathematics | Theory of Computation | Monotone operator | Applications of Mathematics | Engineering, general | Proximal point algorithm | Rate of convergence | Optimization | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MAXIMAL MONOTONE-OPERATORS | CONVERGENCE | COMPUTATIONAL ERRORS | FAMILY | Algorithms | Studies | Origins | Operators | Similarity | Minimization | Hilbert space | Regularization

Convex minimization | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Mathematics | Theory of Computation | Monotone operator | Applications of Mathematics | Engineering, general | Proximal point algorithm | Rate of convergence | Optimization | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MAXIMAL MONOTONE-OPERATORS | CONVERGENCE | COMPUTATIONAL ERRORS | FAMILY | Algorithms | Studies | Origins | Operators | Similarity | Minimization | Hilbert space | Regularization

Journal Article

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, ISSN 0022-3239, 07/2015, Volume 166, Issue 1, pp. 343 - 349

Very recently, the author gave an upper bound on a decreasing positive sequence. And, he made use of it to improve a classical result of Br,zis and Lions...

Convex minimization | MATHEMATICS, APPLIED | Monotone inclusion | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Proximal point algorithm | Rate of convergence | MONOTONE-OPERATORS | Algorithms | Studies | Mathematical analysis

Convex minimization | MATHEMATICS, APPLIED | Monotone inclusion | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Proximal point algorithm | Rate of convergence | MONOTONE-OPERATORS | Algorithms | Studies | Mathematical analysis

Journal Article

Applied Mathematics Letters, ISSN 0893-9659, 12/2016, Volume 62, pp. 55 - 62

The main purpose of this paper is to revisit the proximal point algorithms with over-relaxed -maximal -relaxed monotone mappings for solving variational...

Over-relaxed [formula omitted]-maximal [formula omitted]-monotone mappings | Hilbert spaces | Proximal point algorithms | Variational inclusions | Over-relaxed A-maximal m-monotone mappings | VARIATIONAL-INEQUALITIES | MATHEMATICS, APPLIED | CONVERGENCE | MAPPINGS | MONOTONE-OPERATORS | Algorithms

Over-relaxed [formula omitted]-maximal [formula omitted]-monotone mappings | Hilbert spaces | Proximal point algorithms | Variational inclusions | Over-relaxed A-maximal m-monotone mappings | VARIATIONAL-INEQUALITIES | MATHEMATICS, APPLIED | CONVERGENCE | MAPPINGS | MONOTONE-OPERATORS | Algorithms

Journal Article

Journal of Optimization Theory and Applications, ISSN 0022-3239, 7/2015, Volume 166, Issue 1, pp. 343 - 349

Very recently, the author gave an upper bound on a decreasing positive sequence. And, he made use of it to improve a classical result of Brézis and Lions...

58E35 | Monotone inclusion | 65K15 | Mathematics | Theory of Computation | Proximal point algorithm | Optimization | Convex minimization | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Applications of Mathematics | Engineering, general | Rate of convergence

58E35 | Monotone inclusion | 65K15 | Mathematics | Theory of Computation | Proximal point algorithm | Optimization | Convex minimization | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Applications of Mathematics | Engineering, general | Rate of convergence

Journal Article

SIAM JOURNAL ON OPTIMIZATION, ISSN 1052-6234, 2014, Volume 24, Issue 4, pp. 1614 - 1638

We propose a generalized proximal point algorithm (PPA) in the generic setting of finding a root of a maximal monotone operator. In addition to the classical...

ALTERNATING DIRECTION METHOD | MATHEMATICS, APPLIED | PROGRAMS | LOCAL LINEAR CONVERGENCE | DECOMPOSITION | convex optimization | operator splitting methods | MULTIPLIERS | convergence rate | CONVEX MINIMIZATION | proximal point algorithm | MONOTONE-OPERATORS | Operators | Splitting | Algorithms | Roots | Benchmarking | Optimization | Convergence

ALTERNATING DIRECTION METHOD | MATHEMATICS, APPLIED | PROGRAMS | LOCAL LINEAR CONVERGENCE | DECOMPOSITION | convex optimization | operator splitting methods | MULTIPLIERS | convergence rate | CONVEX MINIMIZATION | proximal point algorithm | MONOTONE-OPERATORS | Operators | Splitting | Algorithms | Roots | Benchmarking | Optimization | Convergence

Journal Article

Optimization Letters, ISSN 1862-4472, 4/2012, Volume 6, Issue 4, pp. 621 - 628

In this paper we construct a proximal point algorithm for maximal monotone operators with appropriate regularization parameters. We obtain the strong...

Computational Intelligence | Operations Research/Decision Theory | Numerical and Computational Physics | Mathematics | Maximal monotone operator | Resolvent identity | Proximal point algorithm | Regularization | Optimization | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | SPACES | OPERATORS

Computational Intelligence | Operations Research/Decision Theory | Numerical and Computational Physics | Mathematics | Maximal monotone operator | Resolvent identity | Proximal point algorithm | Regularization | Optimization | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | SPACES | OPERATORS

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 02/2019, Volume 343, pp. 67 - 89

This paper improves a decomposition-like proximal point algorithm, developed for computing minima of nonsmooth convex functions within a framework of symmetric...

Homogeneous domain of positivity | Compact Lie group | Proximal point algorithm | Hadamard manifold | Weighted Lpcenter of mass | Weighted L | center of mass | MATHEMATICS, APPLIED | Weighted L(P)center of mass | MATRICES | RIEMANNIAN-MANIFOLDS | GEOMETRY | Algorithms

Homogeneous domain of positivity | Compact Lie group | Proximal point algorithm | Hadamard manifold | Weighted Lpcenter of mass | Weighted L | center of mass | MATHEMATICS, APPLIED | Weighted L(P)center of mass | MATRICES | RIEMANNIAN-MANIFOLDS | GEOMETRY | Algorithms

Journal Article

Optimization Letters, ISSN 1862-4472, 05/2018, Volume 13, Issue 4, pp. 1 - 17

In this paper, we propose an asymmetric proximal point algorithm for solving variational inequality problems. The algorithm is asymmetric in the sense that the...

Linear convergence | Asymmetric proximal term | Proximal point algorithm | Inexact APPA | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE

Linear convergence | Asymmetric proximal term | Proximal point algorithm | Inexact APPA | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE

Journal Article

SIAM Journal on Optimization, ISSN 1052-6234, 2016, Volume 26, Issue 4, pp. 2235 - 2260

The purpose of this paper is to establish the almost sure weak ergodic convergence of a sequence of iterates (x(n)) given by x(n+1) = (I+lambda(n)...

Proximal point algorithm | Stochastic approximation | Convex programming | MATHEMATICS, APPLIED | APPROXIMATION | STABILITY | convex programming | NETWORKS | SUM | proximal pointalgorithm | RESOURCE-ALLOCATION | CONVEX | SYSTEMS | stochastic approximation | HILBERT-SPACE | MONOTONE-OPERATORS | FUNCTIONALS

Proximal point algorithm | Stochastic approximation | Convex programming | MATHEMATICS, APPLIED | APPROXIMATION | STABILITY | convex programming | NETWORKS | SUM | proximal pointalgorithm | RESOURCE-ALLOCATION | CONVEX | SYSTEMS | stochastic approximation | HILBERT-SPACE | MONOTONE-OPERATORS | FUNCTIONALS

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 2011, Volume 74, Issue 2, pp. 544 - 555

Several strong convergence results involving two distinct four parameter proximal point algorithms are proved under different sets of assumptions on these...

Regularization method | Weak convergence | Minimizer | Strong convergence | Monotone operator | Proximal point algorithm | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | APPROXIMATION | MATHEMATICS | CONVERGENCE | MONOTONE-OPERATORS | FIXED-POINTS | Algorithms | Errors | Approximation | Equivalence | Norms | Nonlinearity | Regularization | Acceptability | Convergence

Regularization method | Weak convergence | Minimizer | Strong convergence | Monotone operator | Proximal point algorithm | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | APPROXIMATION | MATHEMATICS | CONVERGENCE | MONOTONE-OPERATORS | FIXED-POINTS | Algorithms | Errors | Approximation | Equivalence | Norms | Nonlinearity | Regularization | Acceptability | Convergence

Journal Article

Applied Numerical Mathematics, ISSN 0168-9274, 01/2020, Volume 147, pp. 1 - 18

The classical proximal point algorithm (PPA) requires a metric proximal parameter, which is positive definite and symmetric, because it plays the role of the...

Linear convergence | Worst-case convergence rate | Variational inequality | Nonsymmetric proximal point algorithm | Big data | Algorithms

Linear convergence | Worst-case convergence rate | Variational inequality | Nonsymmetric proximal point algorithm | Big data | Algorithms

Journal Article

Journal of Global Optimization, ISSN 0925-5001, 9/2011, Volume 51, Issue 1, pp. 11 - 26

We present several strong convergence results for the modified, Halpern-type, proximal point algorithm...

Strong convergence | prox-Tikhonov algorithm | Minimizer | Monotone operator | Proximal point algorithm | Optimization | Economics / Management Science | Control conditions | Operations Research/Decision Theory | 47H09 | Convex function | Minimum value | Computer Science, general | 47J25 | 47H05 | Real Functions | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | APPROXIMATION | SPACES | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | CONVERGENCE | FIXED-POINTS | MONOTONE-OPERATORS | Algorithms | Studies

Strong convergence | prox-Tikhonov algorithm | Minimizer | Monotone operator | Proximal point algorithm | Optimization | Economics / Management Science | Control conditions | Operations Research/Decision Theory | 47H09 | Convex function | Minimum value | Computer Science, general | 47J25 | 47H05 | Real Functions | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | APPROXIMATION | SPACES | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | CONVERGENCE | FIXED-POINTS | MONOTONE-OPERATORS | Algorithms | Studies

Journal Article

15.
Full Text
General parameterized proximal point algorithm with applications in statistical learning

International Journal of Computer Mathematics, ISSN 0020-7160, 01/2019, Volume 96, Issue 1, pp. 199 - 215

In the literature, there are a few researches to design some parameters in the proximal point algorithm (PPA), especially for the multi-objective convex...

complexity | statistical learning | Structured convex programming | relaxation step | 90C25 | 65Y20 | 65C60 | proximal point algorithm | MATHEMATICS, APPLIED | SPARSE | DECOMPOSITION | MODEL | ALTERNATING DIRECTION METHOD | CONVEX MINIMIZATION | SPLITTING METHOD | LOW-RANK | Multiple objective analysis | Computational geometry | State of the art | Design parameters | Algorithms | Machine learning | Convexity | Parameterization | Matrix methods | Optimization | Convergence | Mathematical programming | Mathematics - Optimization and Control

complexity | statistical learning | Structured convex programming | relaxation step | 90C25 | 65Y20 | 65C60 | proximal point algorithm | MATHEMATICS, APPLIED | SPARSE | DECOMPOSITION | MODEL | ALTERNATING DIRECTION METHOD | CONVEX MINIMIZATION | SPLITTING METHOD | LOW-RANK | Multiple objective analysis | Computational geometry | State of the art | Design parameters | Algorithms | Machine learning | Convexity | Parameterization | Matrix methods | Optimization | Convergence | Mathematical programming | Mathematics - Optimization and Control

Journal Article

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, ISSN 0022-3239, 09/2019, Volume 182, Issue 3, pp. 1019 - 1049

We show that Dykstra's splitting for projecting onto the intersection of convex sets can be extended to minimize the sum of convex functions and a regularizing...

MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | GRADIENT DESCENT METHOD | MINIMIZATION | DECOMPOSITION | CONVERGENCE | Block coordinate minimization | Proximal point algorithm | LINEAR REGULARITY | Dykstra's splitting | LEAST-SQUARES | Algorithms

MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | GRADIENT DESCENT METHOD | MINIMIZATION | DECOMPOSITION | CONVERGENCE | Block coordinate minimization | Proximal point algorithm | LINEAR REGULARITY | Dykstra's splitting | LEAST-SQUARES | Algorithms

Journal Article

Journal of Optimization Theory and Applications, ISSN 0022-3239, 9/2019, Volume 182, Issue 3, pp. 1019 - 1049

We show that Dykstra’s splitting for projecting onto the intersection of convex sets can be extended to minimize the sum of convex functions and a regularizing...

Dykstra’s splitting | 68Q25 | 65K05 | Mathematics | Theory of Computation | Proximal point algorithm | Optimization | Calculus of Variations and Optimal Control; Optimization | 90C25 | Operations Research/Decision Theory | Block coordinate minimization | Applications of Mathematics | Engineering, general | 47J25 | Quadratic equations | Computational geometry | Splitting | Algorithms | Convexity | Convex analysis | Goal programming

Dykstra’s splitting | 68Q25 | 65K05 | Mathematics | Theory of Computation | Proximal point algorithm | Optimization | Calculus of Variations and Optimal Control; Optimization | 90C25 | Operations Research/Decision Theory | Block coordinate minimization | Applications of Mathematics | Engineering, general | 47J25 | Quadratic equations | Computational geometry | Splitting | Algorithms | Convexity | Convex analysis | Goal programming

Journal Article

Journal of Global Optimization, ISSN 0925-5001, 12/2015, Volume 63, Issue 4, pp. 797 - 810

An extension of a proximal point algorithm for difference of two convex functions is presented in the context of Riemannian manifolds of nonposite sectional...

49M30 | Nonconvex optimization | Hadamard manifolds | Mathematics | 90C26 | 90C48 | Operation Research/Decision Theory | Computer Science, general | Proximal point algorithm | DC functions | Optimization | Real Functions | MATHEMATICS, APPLIED | VECTOR-FIELDS | VARIATIONAL-INEQUALITIES | NEWTONS METHOD | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MONOTONE | CONVERGENCE | OPTIMIZATION | RIEMANNIAN-MANIFOLDS | Algorithms | Studies | Optimization algorithms | Topological manifolds | Mathematical analysis | Manifolds | Maximization | Clusters | Minimization | Curvature

49M30 | Nonconvex optimization | Hadamard manifolds | Mathematics | 90C26 | 90C48 | Operation Research/Decision Theory | Computer Science, general | Proximal point algorithm | DC functions | Optimization | Real Functions | MATHEMATICS, APPLIED | VECTOR-FIELDS | VARIATIONAL-INEQUALITIES | NEWTONS METHOD | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MONOTONE | CONVERGENCE | OPTIMIZATION | RIEMANNIAN-MANIFOLDS | Algorithms | Studies | Optimization algorithms | Topological manifolds | Mathematical analysis | Manifolds | Maximization | Clusters | Minimization | Curvature

Journal Article

Optimization Letters, ISSN 1862-4472, 10/2018, Volume 12, Issue 7, pp. 1589 - 1608

In this paper, we develop a parameterized proximal point algorithm (P-PPA) for solving a class of separable convex programming problems subject to linear and...

Separable convex programming | Global convergence | Computational Intelligence | Statistical learning | Operations Research/Decision Theory | Mathematics | Numerical and Computational Physics, Simulation | Proximal point algorithm | Optimization | BREGMAN FUNCTIONS | MATHEMATICS, APPLIED | DECOMPOSITION | SPARSE | MULTIPLIERS | MINIMIZATION PROBLEMS | ALTERNATING DIRECTION METHOD | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | SPLITTING METHOD | OPERATORS | Mathematics - Optimization and Control

Separable convex programming | Global convergence | Computational Intelligence | Statistical learning | Operations Research/Decision Theory | Mathematics | Numerical and Computational Physics, Simulation | Proximal point algorithm | Optimization | BREGMAN FUNCTIONS | MATHEMATICS, APPLIED | DECOMPOSITION | SPARSE | MULTIPLIERS | MINIMIZATION PROBLEMS | ALTERNATING DIRECTION METHOD | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | SPLITTING METHOD | OPERATORS | Mathematics - Optimization and Control

Journal Article

Quaestiones Mathematicae, ISSN 1607-3606, 10/2019, Volume 42, Issue 8, pp. 1065 - 1078

In this work, we introduce a generalized contraction proximal point algorithm and use it to approximate common zeros of maximal monotone operators A and B in a...

nonexpansive map | alternating method | contraction proximal point algorithm | resolvent operator | 47H09 | Maximal monotone operator | 47J25 | 47H05

nonexpansive map | alternating method | contraction proximal point algorithm | resolvent operator | 47H09 | Maximal monotone operator | 47J25 | 47H05

Journal Article

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