4.5 Article

An Adaptive Alternating Direction Method of Multipliers

相关参考文献

注意:仅列出部分参考文献,下载原文获取全部文献信息。
Article Operations Research & Management Science

Conical averagedness and convergence analysis of fixed point algorithms

Sedi Bartz et al.

Summary: In this study, the properties of conically averaged operators are systematically investigated, especially their stability under different conditions, and then utilized to analyze the convergence of several fixed point algorithms. This research unifies previous studies and provides new insights into these topics.

JOURNAL OF GLOBAL OPTIMIZATION (2022)

Article Computer Science, Software Engineering

Generalized monotone operators and their averaged resolvents

Heinz H. Bauschke et al.

Summary: The correspondence between the monotonicity of a (possibly) set-valued operator and the firm nonexpansiveness of its resolvent plays a key role in convergence analysis of optimization algorithms. Firmly nonexpansive operators are a subclass of averaged operators, and the new notion of conically nonexpansive operators is introduced in this paper. Averaged operators are characterized as resolvents of comonotone operators under appropriate scaling, and proximal point mappings associated with hypoconvex functions are characterized as cocoercive operators or displacement mappings of conically nonexpansive operators. Several examples are provided to illustrate the analysis and demonstrate the tightness of the results.

MATHEMATICAL PROGRAMMING (2021)

Article Mathematics, Applied

ADAPTIVE DOUGLAS-RACHFORD SPLITTING ALGORITHM FROM A YOSIDA APPROXIMATION STANDPOINT

Zihan Liu et al.

Summary: The article introduces the adaptive Douglas-Rachford splitting algorithm, which iteratively applies the operator T to solve the inclusion problem zer(A + B) and extends the domain of indices to encompass a forward-backward splitting algorithm. Convergence results are proved for different combinations of operators, with a better convergence rate obtained under the "monotone + comonotone" assumption compared to the classical algorithm.

SIAM JOURNAL ON OPTIMIZATION (2021)

Article Operations Research & Management Science

A continuous dynamical splitting method for solving 'strongly plus weakly' convex programming problems

Ming Zhu et al.

OPTIMIZATION (2020)

Article Operations Research & Management Science

Demiclosedness Principles for Generalized Nonexpansive Mappings

Sedi Bartz et al.

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS (2020)

Article Mathematics, Applied

ADMM for monotone operators: convergence analysis and rates

Radu Ioan Bot et al.

ADVANCES IN COMPUTATIONAL MATHEMATICS (2019)

Article Mathematics, Applied

Global Convergence of ADMM in Nonconvex Nonsmooth Optimization

Yu Wang et al.

JOURNAL OF SCIENTIFIC COMPUTING (2019)

Article Operations Research & Management Science

Douglas-Rachford splitting and ADMM for pathological convex optimization

Ernest K. Ryu et al.

COMPUTATIONAL OPTIMIZATION AND APPLICATIONS (2019)

Article Mathematics, Applied

Path-following and semismooth Newton methods for the variational inequality arising from two membranes problem

Shougui Zhang et al.

JOURNAL OF INEQUALITIES AND APPLICATIONS (2019)

Article Mathematics, Applied

ADAPTIVE DOUGLAS-RACHFORD SPLITTING ALGORITHM FOR THE SUM OF TWO OPERATORS

Minh N. Dao et al.

SIAM JOURNAL ON OPTIMIZATION (2019)

Article Computer Science, Information Systems

Convergence of multi-block Bregman ADMM for nonconvex composite problems

Fenghui Wang et al.

SCIENCE CHINA-INFORMATION SCIENCES (2018)

Article Operations Research & Management Science

A note on the convergence of ADMM for linearly constrained convex optimization problems

Liang Chen et al.

COMPUTATIONAL OPTIMIZATION AND APPLICATIONS (2017)

Article Mathematics, Applied

CONVERGENCE ANALYSIS OF DOUGLAS-RACHFORD SPLITTING METHOD FOR STRONGLY plus WEAKLY CONVEX PROGRAMMING

Ke Guo et al.

SIAM JOURNAL ON NUMERICAL ANALYSIS (2017)

Article Automation & Control Systems

ON THE CONVEXITY OF PIECEWISE-DEFINED FUNCTIONS

Heinz H. Bauschke et al.

ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS (2016)

Article Computer Science, Artificial Intelligence

Local Linear Convergence of the ADMM/Douglas-Rachford Algorithms without Strong Convexity and Application to Statistical Imaging

Timo Aspelmeier et al.

SIAM JOURNAL ON IMAGING SCIENCES (2016)

Article Mathematics, Applied

CONVERGENCE ANALYSIS OF ALTERNATING DIRECTION METHOD OF MULTIPLIERS FOR A FAMILY OF NONCONVEX PROBLEMS

Mingyi Hong et al.

SIAM JOURNAL ON OPTIMIZATION (2016)

Article Automation & Control Systems

ON THE CONVEXITY OF PIECEWISE-DEFINED FUNCTIONS

Heinz H. Bauschke et al.

ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS (2016)

Article Computer Science, Artificial Intelligence

The Primal-Dual Hybrid Gradient Method for Semiconvex Splittings

Thomas Moellenhoff et al.

SIAM JOURNAL ON IMAGING SCIENCES (2015)

Article Mathematics, Applied

GLOBAL CONVERGENCE OF SPLITTING METHODS FOR NONCONVEX COMPOSITE OPTIMIZATION

Guoyin Li et al.

SIAM JOURNAL ON OPTIMIZATION (2015)

Proceedings Paper Operations Research & Management Science

Projection Methods: Swiss Army Knives for Solving Feasibility and Best Approximation Problems with Halfspaces

Heinz H. Bauschke et al.

INFINITE PRODUCTS OF OPERATORS AND THEIR APPLICATIONS (2015)

Article Mathematics

Attouch-Thera duality revisited: Paramonotonicity and operator splitting

Heinz H. Bauschke et al.

JOURNAL OF APPROXIMATION THEORY (2012)

Article Mathematics, Applied

Dualization of Signal Recovery Problems

Patrick L. Combettes et al.

SET-VALUED AND VARIATIONAL ANALYSIS (2010)

Article Mathematics, Interdisciplinary Applications

Signal recovery by proximal forward-backward splitting

PL Combettes et al.

MULTISCALE MODELING & SIMULATION (2005)

Article Automation & Control Systems

Proximal methods for cohypomonotone operators

PL Combettes et al.

SIAM JOURNAL ON CONTROL AND OPTIMIZATION (2004)