Fixed point theory and applications (Hindawi Publishing Corporation), ISSN 1687-1820, 12/2014, Volume 2014, Issue 1, pp. 1 - 15

In this paper, we investigate a splitting algorithm for treating monotone operators...

maximal monotone operator | Mathematical and Computational Biology | fixed point | Analysis | Mathematics, general | nonexpansive mapping | Mathematics | zero point | Applications of Mathematics | Topology | Differential Geometry | proximal point algorithm | Maximal monotone operator | Proximal point algorithm | Zero point | Nonexpansive mapping | Fixed point | Physical Sciences | Mathematics, Applied | Science & Technology | Fixed point theory | Usage | Hilbert space | Contraction operators | Operators | Theorems | Splitting | Algorithms | Convergence

maximal monotone operator | Mathematical and Computational Biology | fixed point | Analysis | Mathematics, general | nonexpansive mapping | Mathematics | zero point | Applications of Mathematics | Topology | Differential Geometry | proximal point algorithm | Maximal monotone operator | Proximal point algorithm | Zero point | Nonexpansive mapping | Fixed point | Physical Sciences | Mathematics, Applied | Science & Technology | Fixed point theory | Usage | Hilbert space | Contraction operators | Operators | Theorems | Splitting | Algorithms | Convergence

Journal Article

Mathematical programming, ISSN 1436-4646, 08/2011, Volume 137, Issue 1-2, pp. 91 - 129

...–backward splitting algorithm, the gradient projection and some proximal regularization of the Gauss–Seidel method in a nonconvex setting. Our results are illustrated through feasibility problems, or iterative thresholding procedures for compressive sensing.

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 | Operations Research & Management Science | Physical Sciences | Technology | Computer Science | Computer Science, Software Engineering | Mathematics, Applied | Science & Technology | 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 | Operations Research & Management Science | Physical Sciences | Technology | Computer Science | Computer Science, Software Engineering | Mathematics, Applied | Science & Technology | Methods | Algorithms | Studies | Algebra | Analysis | Data smoothing | Optimization | Mathematical programming | Splitting | Gauss-Seidel method | Mathematical analysis | Minimization | Descent | Convergence

Journal Article

Journal of scientific computing, ISSN 1573-7691, 08/2010, Volume 46, Issue 1, pp. 20 - 46

In this paper, we propose a unified primal-dual algorithm framework for two classes of problems that arise from various signal and image processing applications...

ℓ 1 minimization | Computational Mathematics and Numerical Analysis | Algorithms | Theoretical, Mathematical and Computational Physics | Appl.Mathematics/Computational Methods of Engineering | Inexact Uzawa methods | Mathematics | Bregman iteration | Proximal point iteration | Saddle point | minimization | Physical Sciences | Mathematics, Applied | Science & Technology | Equipment and supplies | Image processing | Analysis | Computer programs | Mathematical models | Iterative methods | Joints | Optimization | Convergence | Rice

ℓ 1 minimization | Computational Mathematics and Numerical Analysis | Algorithms | Theoretical, Mathematical and Computational Physics | Appl.Mathematics/Computational Methods of Engineering | Inexact Uzawa methods | Mathematics | Bregman iteration | Proximal point iteration | Saddle point | minimization | Physical Sciences | Mathematics, Applied | Science & Technology | Equipment and supplies | Image processing | Analysis | Computer programs | Mathematical models | Iterative methods | Joints | Optimization | Convergence | Rice

Journal Article

Journal of optimization theory and applications, ISSN 1573-2878, 11/2014, Volume 166, Issue 1, pp. 343 - 349

... of Brézis and Lions concerning the proximal point algorithm for monotone inclusion in an infinite-dimensional Hilbert space...

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 | Operations Research & Management Science | Physical Sciences | Mathematics, Applied | Technology | Science & Technology | Algorithms | Studies | Mathematical analysis

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 | Operations Research & Management Science | Physical Sciences | Mathematics, Applied | Technology | Science & Technology | Algorithms | Studies | Mathematical analysis

Journal Article

Journal of optimization theory and applications, ISSN 1573-2878, 06/2013, 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 Hilbert space...

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 | Operations Research & Management Science | Physical Sciences | Mathematics, Applied | Technology | Science & Technology | 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 | Operations Research & Management Science | Physical Sciences | Mathematics, Applied | Technology | Science & Technology | Algorithms | Studies | Origins | Operators | Similarity | Minimization | Hilbert space | Regularization

Journal Article

Numerical algorithms, ISSN 1572-9265, 08/2017, 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...

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 | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Medical colleges | Analysis | Resveratrol | Fixed points (mathematics) | Asymptotic properties | Convergence

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 | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Medical colleges | Analysis | Resveratrol | Fixed points (mathematics) | Asymptotic properties | Convergence

Journal Article

Optimization letters, ISSN 1862-4480, 02/2011, Volume 6, Issue 4, pp. 621 - 628

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

Computational Intelligence | Operations Research/Decision Theory | Numerical and Computational Physics | Mathematics | Maximal monotone operator | Resolvent identity | Proximal point algorithm | Regularization | Optimization | Operations Research & Management Science | Physical Sciences | Mathematics, Applied | Technology | Science & Technology | Algorithms

Computational Intelligence | Operations Research/Decision Theory | Numerical and Computational Physics | Mathematics | Maximal monotone operator | Resolvent identity | Proximal point algorithm | Regularization | Optimization | Operations Research & Management Science | Physical Sciences | Mathematics, Applied | Technology | Science & Technology | Algorithms

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 | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Probability | Optimization and Control | Statistics | Machine Learning

Proximal point algorithm | Stochastic approximation | Convex programming | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Probability | Optimization and Control | Statistics | Machine Learning

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 convex constraints...

Separable convex programming | Global convergence | Computational Intelligence | Statistical learning | Operations Research/Decision Theory | Mathematics | Numerical and Computational Physics, Simulation | Proximal point algorithm | Optimization | Operations Research & Management Science | Physical Sciences | Mathematics, Applied | Technology | Science & Technology | Algorithms | 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 | Operations Research & Management Science | Physical Sciences | Mathematics, Applied | Technology | Science & Technology | Algorithms | Mathematics - Optimization and Control

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
$${x_{n+1}=\alpha_{n}u+(1-\alpha_{n})J_{\beta_n}x_n+e_{n...

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 | Operations Research & Management Science | Physical Sciences | Mathematics | Mathematics, Applied | Technology | Science & Technology | 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 | Operations Research & Management Science | Physical Sciences | Mathematics | Mathematics, Applied | Technology | Science & Technology | Algorithms | Studies

Journal Article

Journal of optimization theory and applications, ISSN 0022-3239, 6/2012, Volume 153, Issue 3, pp. 769 - 778

In this paper, we obtain some results on the boundedness and asymptotic behavior of the sequence generated by the proximal point algorithm without summability assumption on the error sequence...

Maximal monotone operators | Asymptotic behavior | Mathematics | Theory of Computation | Optimization | Proximal-point algorithm | Monotone bifunctions | Calculus of Variations and Optimal Control; Optimization | Equilibrium problems | Operations Research/Decision Theory | Engineering, general | Applications of Mathematics | Rate of convergence | Operations Research & Management Science | Physical Sciences | Mathematics, Applied | Technology | Science & Technology | Algorithms | Errors | Asymptotic properties | Convergence

Maximal monotone operators | Asymptotic behavior | Mathematics | Theory of Computation | Optimization | Proximal-point algorithm | Monotone bifunctions | Calculus of Variations and Optimal Control; Optimization | Equilibrium problems | Operations Research/Decision Theory | Engineering, general | Applications of Mathematics | Rate of convergence | Operations Research & Management Science | Physical Sciences | Mathematics, Applied | Technology | Science & Technology | Algorithms | Errors | Asymptotic properties | Convergence

Journal Article

Journal of machine learning research, ISSN 1532-4435, 08/2018, Volume 19, pp. 1 - 38

.... Focusing on Gaussian graphical models, we introduce an approximate majorize-minimize (MM) algorithm that can be useful for computing change-points in large graphical models...

Change-points | Gaussian graphical models | Proximal gradient | Stochastic optimization | Simulated annealing | Automation & Control Systems | Computer Science, Artificial Intelligence | Technology | Computer Science | Science & Technology

Change-points | Gaussian graphical models | Proximal gradient | Stochastic optimization | Simulated annealing | Automation & Control Systems | Computer Science, Artificial Intelligence | Technology | Computer Science | Science & Technology

Journal Article

Fixed point theory and applications (Hindawi Publishing Corporation), ISSN 1687-1820, 12/2014, Volume 2014, Issue 1, pp. 1 - 11

A proximal point algorithm with double computational errors for treating zero points of accretive operators is investigated...

accretive operator | Mathematical and Computational Biology | fixed point | Analysis | Mathematics, general | nonexpansive mapping | Mathematics | zero point | Applications of Mathematics | Topology | Differential Geometry | proximal point algorithm | Proximal point algorithm | Zero point | Accretive operator | Nonexpansive mapping | Fixed point | Physical Sciences | Mathematics, Applied | Science & Technology | Fixed point theory | Usage | Convergence (Mathematics) | Contraction operators

accretive operator | Mathematical and Computational Biology | fixed point | Analysis | Mathematics, general | nonexpansive mapping | Mathematics | zero point | Applications of Mathematics | Topology | Differential Geometry | proximal point algorithm | Proximal point algorithm | Zero point | Accretive operator | Nonexpansive mapping | Fixed point | Physical Sciences | Mathematics, Applied | Science & Technology | Fixed point theory | Usage | Convergence (Mathematics) | Contraction operators

Journal Article

Journal of optimization theory and applications, ISSN 0022-3239, 5/2008, Volume 137, Issue 2, pp. 411 - 417

Let A be a maximal monotone operator in a real Hilbert space H and let {u
n
} be the sequence in H given by the proximal point algorithm, defined by u
n
=(I+c
n
A)−1(u
n−1−f
n
), ∀
n≥1, with u
0=z, where c
n
>0 and f
n
∈H...

Maximal monotone operators | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Mathematics | Theory of Computation | Ergodic theorems | Engineering, general | Applications of Mathematics | Optimization | Proximal-point algorithms | Variational inequalities | Asymptotic centers | Operations Research & Management Science | Physical Sciences | Mathematics, Applied | Technology | Science & Technology | Algorithms | Studies | Optimization algorithms | Asymptotic methods | Operators | Hilbert space

Maximal monotone operators | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Mathematics | Theory of Computation | Ergodic theorems | Engineering, general | Applications of Mathematics | Optimization | Proximal-point algorithms | Variational inequalities | Asymptotic centers | Operations Research & Management Science | Physical Sciences | Mathematics, Applied | Technology | Science & Technology | Algorithms | Studies | Optimization algorithms | Asymptotic methods | Operators | Hilbert space

Journal Article

Journal of inequalities and applications, ISSN 1025-5834, 12/2013, Volume 2013, Issue 1, pp. 1 - 11

... in Hilbert spaces and the convergence analysis of iterative sequences generated by the over-relaxed
-proximal point algorithm frameworks with errors, which generalize...

convergence analysis | generalized proximal operator technique | Analysis | over-relaxed -proximal point algorithm frameworks with errors | Mathematics, general | Mathematics | monotonicity | general variational inclusion problem | Applications of Mathematics | General variational inclusion problem | Generalized proximal operator technique | (A,η,m)-monotonicity | Over-relaxed (A,η,m)-proximal point algorithm frameworks with errors | Convergence analysis | Physical Sciences | Mathematics, Applied | Science & Technology | Operators | Algorithms | Error analysis | Approximation | Mathematical analysis | Inequalities | Inclusions | Convergence

convergence analysis | generalized proximal operator technique | Analysis | over-relaxed -proximal point algorithm frameworks with errors | Mathematics, general | Mathematics | monotonicity | general variational inclusion problem | Applications of Mathematics | General variational inclusion problem | Generalized proximal operator technique | (A,η,m)-monotonicity | Over-relaxed (A,η,m)-proximal point algorithm frameworks with errors | Convergence analysis | Physical Sciences | Mathematics, Applied | Science & Technology | Operators | Algorithms | Error analysis | Approximation | Mathematical analysis | Inequalities | Inclusions | Convergence

Journal Article