Article
Mathematics, Applied
Jianchao Bai, Yuxue Ma, Hao Sun, Miao Zhang
Summary: This paper investigates a convex optimization problem with multi-block variables and separable structures. A partial LQP-based ADMM algorithm is proposed, and the convergence and convergence rate are analyzed using a prediction-correction approach.
APPLIED NUMERICAL MATHEMATICS
(2021)
Article
Operations Research & Management Science
Hongmei Chen, Guoyong Gu, Junfeng Yang
Summary: Researchers propose a new variant of the classical ADMM, called golden ratio proximal ADMM (GrpADMM), which achieves advantages in problem structures and global convergence.
JOURNAL OF GLOBAL OPTIMIZATION
(2023)
Article
Chemistry, Physical
Xiaodong Wei, Chao Sun, Qiang Ren, Feikun Zhou, Weiwei Huo, Fengchun Sun
Summary: This paper proposes a method based on the ADMM algorithm to solve the energy management problem for fuel cell vehicles, demonstrating faster computation speed and higher accuracy through simulation results.
INTERNATIONAL JOURNAL OF HYDROGEN ENERGY
(2021)
Article
Engineering, Multidisciplinary
Benxin Zhang, Guopu Zhu, Zhibin Zhu, Sam Kwong
Summary: This paper proposes a nonconvex log total variation model for image restoration, and presents a specific alternating direction method of multipliers to solve the model. Experimental results demonstrate that the proposed method is effective in image denoising, deblurring, computed tomography, magnetic resonance imaging, and image super-resolution.
APPLIED MATHEMATICAL MODELLING
(2023)
Article
Mathematics, Applied
Jianwen Peng, Xueqing Zhang
Summary: This paper proves important inequalities and establishes local and global linear convergence rates for GADMM in solving convex optimization problems.
JOURNAL OF NONLINEAR AND CONVEX ANALYSIS
(2022)
Article
Mathematics, Applied
Haoran Zhu, Liping Zhang
Summary: This paper investigates the solution methods for the tensor complementarity problem (TCP) and proposes an ADMM method, proving that the method has global convergence and linear convergence rate when the involved multilinear mapping is monotone. Preliminary numerical results indicate that the proposed ADMM method is promising and effective.
COMPUTATIONAL & APPLIED MATHEMATICS
(2021)
Article
Engineering, Electrical & Electronic
Jiaojiao Zhang, Huikang Liu, Anthony Man-Cho Sow, Qing Ling
Summary: This paper investigates the problem of minimizing a sum of convex composite functions over a decentralized network. The proposed penalty ADMM method shows sublinear convergence for convex private functions and linear convergence when the smooth parts are strongly convex. Numerical results confirm the theoretical analyses and demonstrate the advantages of PAD over existing state-of-the-art algorithms.
IEEE TRANSACTIONS ON SIGNAL PROCESSING
(2021)
Article
Mathematics
Zhangquan Wang, Shanshan Huo, Xinlong Xiong, Ke Wang, Banteng Liu
Summary: This paper proposes an adaptive parameter selection method based on the ADMM, which decomposes a convex model-fitting problem into a set of sub-problems that can be executed in parallel. The effectiveness of the algorithm is verified through experiments on eight classification datasets, showing improved speed of data processing and increased parallelism.
Article
Engineering, Civil
Jun Ma, Zilong Cheng, Xiaoxue Zhang, Masayoshi Tomizuka, Tong Heng Lee
Summary: In this paper, a method using iterative linear quadratic regulator (iLQR) and alternating direction method of multipliers (ADMM) for motion planning in the context of autonomous driving is proposed. The method achieves high computation efficiency under various constraints and enables real-time computation and implementation, providing additional safety to on-road driving tasks.
IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS
(2022)
Article
Engineering, Mechanical
Miantao Chao, Liqun Liu
Summary: In this paper, a dynamical ADMM is proposed for two-block separable optimization problems. The classical ADMM is obtained after discretizing the dynamical system in time. Under appropriate conditions, it is proved that the trajectory asymptotically converges to a saddle point of the Lagrangian function. When the coefficient matrices in the constraint are identity matrices, a worst-case O(1/t) convergence rate in the ergodic sense is proven.
NONLINEAR DYNAMICS
(2023)
Article
Computer Science, Artificial Intelligence
Jia Hu, Tiande Guo, Tong Zhao
Summary: This paper introduces a faster stochastic alternating direction method for solving large scale convex composite problems, incorporating a randomization scheme to reduce computational time. The method is shown to be effective in numerical experiments and has unified the stochastic ADMM for solving general convex and strongly convex composite problems.
APPLIED INTELLIGENCE
(2022)
Article
Operations Research & Management Science
Zehui Jia, Xue Gao, Xingju Cai, Deren Han
Summary: In this paper, the convergence rate of the alternating direction method of multipliers for solving nonconvex separable optimization problems is considered. It is proven that the sequence generated by this method converges locally to a critical point of the nonconvex optimization problem with a linear convergence rate. Results are illustrated through the application of this method to nonconvex quadratic programming problems and comparison with other state-of-the-art algorithms.
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
(2021)
Article
Operations Research & Management Science
Danqing Zhou, Haiwen Xu, Junfeng Yang
Summary: PADMC is a new variant of PADMM that constructs proximal centers by convex combinations of the iterates, which can take advantage of problem structures and preserves the desirable properties of classical PADMM. We establish iterate convergence and provide convergence rate results for different scenarios. Two fast variants are also proposed to handle specific cases.
ASIA-PACIFIC JOURNAL OF OPERATIONAL RESEARCH
(2023)
Article
Operations Research & Management Science
Sedi Bartz, Ruben Campoy, Hung M. Phan
Summary: This paper proposes and studies an adaptive version of ADMM for the case where the objective function is the sum of a strongly convex function and a weakly convex function. By combining generalized notions of convexity and penalty parameters with the convexity constants of the functions, we prove convergence of the algorithm under natural assumptions.
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
(2022)
Article
Mathematics, Applied
Sergei Chubanov
Summary: The proposed algorithm in this article is an advancement of alternating projections method for convex programming. It can efficiently solve combinatorial optimization problems in polynomial time. Additionally, it is a Fully polynomial time approximation Scheme for a wide range of optimization problems with an exponential or infinite number of constraints.
SIAM JOURNAL ON OPTIMIZATION
(2021)
Article
Computer Science, Theory & Methods
Tianyi Lin, Shiqian Ma, Shuzhong Zhang
FOUNDATIONS OF COMPUTATIONAL MATHEMATICS
(2017)
Article
Mathematics, Applied
Tianyi Lin, Shiqian Ma, Shuzhong Zhang
JOURNAL OF SCIENTIFIC COMPUTING
(2016)
Article
Computer Science, Artificial Intelligence
Yinqing Xu, Qian Yu, Wai Lam, Tianyi Lin
KNOWLEDGE AND INFORMATION SYSTEMS
(2017)
Article
Mathematics, Applied
Tianyi Lin, Shiqian Ma, Shuzhong Zhang
JOURNAL OF SCIENTIFIC COMPUTING
(2018)
Article
Computer Science, Artificial Intelligence
Tianyi Lin, Linbo Qiao, Teng Zhang, Jiashi Feng, Bofeng Zhang
Article
Computer Science, Artificial Intelligence
Linbo Qiao, Tianyi Lin, Qi Qin, Xicheng Lu
Article
Operations Research & Management Science
Bo Jiang, Tianyi Lin, Shiqian Ma, Shuzhong Zhang
COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
(2019)
Article
Computer Science, Software Engineering
Tianyi Lin, Shiqian Ma, Yinyu Ye, Shuzhong Zhang
Summary: In this paper, a new method named ABIP based on Alternating Direction Method of Multipliers (ADMM) is proposed, which inherits stability from IPM and scalability from ADMM. ABIP approximates the minimization of the log-barrier penalty function using ADMM in the framework, solving large-scale LP problems.
OPTIMIZATION METHODS & SOFTWARE
(2021)
Article
Computer Science, Software Engineering
Tianyi Lin, Michael Jordan
Summary: The study presents an optimal tensor algorithm from a control-theoretic perspective, proving the existence and uniqueness of local and global solutions, analyzing convergence properties, and demonstrating the fundamental role of feedback control in optimal acceleration. The analysis shows that all discussed p-th order optimal tensor algorithms minimize the squared gradient norm at a rate of O(k(-3p)), complementing recent studies in the field.
MATHEMATICAL PROGRAMMING
(2022)
Article
Operations Research & Management Science
Tianyi Lin, Michael I. Jordan
Summary: We propose a new dynamical system with closed-loop control in a Hilbert space H to study the acceleration phenomenon for monotone inclusion problems. The control law is governed by the operator I - (I + lambda(t)A)(-1), where lambda(center dot) is tuned by solving an algebraic equation. We prove the existence and uniqueness of a global solution and establish convergence rates for the trajectories under various conditions.
MATHEMATICS OF OPERATIONS RESEARCH
(2023)
Proceedings Paper
Acoustics
Xin Guo, Johnny Hong, Tianyi Lin, Nan Yang
Summary: This paper introduces a new class of Relaxed Wasserstein distances by generalizing Wasserstein-1 distance with Bregman cost functions. Experiments demonstrate that Relaxed WGANs with Kullback-Leibler cost function outperform other competing approaches in terms of statistical flexibility and efficient approximations.
2021 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING (ICASSP 2021)
(2021)
Proceedings Paper
Computer Science, Artificial Intelligence
Tianyi Lin, Zeyu Zheng, Elynn Y. Chen, Marco Cuturi, Michael Jordan
Summary: This study explores the statistical properties of projection robust OT, introduces the IPRW distance as an alternative to PRW, and shows that both PRW and IPRW distances outperform Wasserstein distances in high-dimensional inference tasks.
24TH INTERNATIONAL CONFERENCE ON ARTIFICIAL INTELLIGENCE AND STATISTICS (AISTATS)
(2021)
Proceedings Paper
Automation & Control Systems
Tianyi Lin, Chengyou Fan, Mengdi Wang, Michael I. Jordan
2020 AMERICAN CONTROL CONFERENCE (ACC)
(2020)
Article
Mathematics, Applied
Bo Jiang, Tianyi Lin, Shuzhong Zhang
SIAM JOURNAL ON OPTIMIZATION
(2020)
Proceedings Paper
Computer Science, Information Systems
Tianyi Lin, Siyuan Zhang, Hong Cheng
CIKM'16: PROCEEDINGS OF THE 2016 ACM CONFERENCE ON INFORMATION AND KNOWLEDGE MANAGEMENT
(2016)