Article
Engineering, Multidisciplinary
Liping Ma, Lijing Zhao, Xiaodong Wang
Summary: Based on our previous study, the combination of the semi-Lagrangian method and the element free Galerkin method has been proven to be effective in solving convection-dominated problems. The meshless feature simplifies the backtracking process in the semi-Lagrangian method. However, the moving least squares approximation in the element free Galerkin method is somewhat costly. To address this issue, this paper presents an iteration-free backtracking method based on Taylor expansion, which greatly improves computational efficiency without sacrificing accuracy when compared to other backtracking methods.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2023)
Article
Operations Research & Management Science
Yuan Shen, Xingying Zhang, Xiayang Zhang
Summary: The Alternating Direction Method of Multipliers (ADMM) is a classical effective method for solving convex optimization problems, but its convergence may not be guaranteed in the case of multiple blocks. This paper proposes a new partial PPA block-wise ADMM method, which shows empirically effectiveness in solving problems compared to other efficient ADMM-based algorithms.
Article
Mathematics
Sina Etemad, Albert Shikongo, Kolade M. Owolabi, Brahim Tellab, Ibrahim Avci, Shahram Rezapour, Ravi P. Agarwal
Summary: This study introduces a new mathematical modeling approach using hybrid generalized fractal-fractional derivatives, focusing on a five-compartmental system of differential equations. A smoking cessation model is designed and its dynamical behaviors are analyzed by considering parameters such as fractal dimension and fractional order. The existence and uniqueness of solutions are investigated, stability properties are proven, and equilibrium points and asymptotically stable solutions are obtained. All findings are illustrated through numerical algorithms and graphs, discussing the behaviors of relevant solutions in the fractal-fractional system.
Article
Thermodynamics
Suheil Khuri, Reem Assadi
Summary: The purpose of this paper is to find approximate solutions for a general class of fractional order boundary value problems that arise in engineering applications. A newly developed semi-analytical scheme is applied to find these approximate solutions. The method, which is an extension of the variation iteration method, yields accurate approximations with uniform error distributions throughout their domain.
INTERNATIONAL JOURNAL OF NUMERICAL METHODS FOR HEAT & FLUID FLOW
(2023)
Article
Mathematics, Applied
Jiawei Xu, Miantao Chao
Summary: This paper investigates an inertial Bregman generalized alternating direction method of multiplies for solving nonconvex optimization with linear constraints. The iterative schemes are formulated based on the proximal alternating direction method of multipliers and its inertial variant, introducing a proximal term via Bregman distance. Under certain assumptions, it is proven that the iterative sequence generated by the algorithm converges to a critical point of the problem being considered. Preliminary numerical results on signal recovery and SCAD penalty problems are reported to demonstrate the efficiency of the proposed method.
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
(2022)
Article
Operations Research & Management Science
Hamid Gazmeh, Eskandar Naraghirad
Summary: This paper discusses the split common null point problem in two Banach spaces and proves strong convergence theorems using the Bregman generalized resolvents of maximal monotone operators. A new technique based on the Bregman distance induced by a Bregman function is introduced, improving and extending many recent results in the literature.
Article
Computer Science, Artificial Intelligence
Jianrui Chen, Yanqing Lu, Fanhua Shang, Yuyang Wang
Summary: This paper proposes a fuzzy matrix decomposition and trace norm minimization method based on forgetting functions and users' multi-attribute features to effectively address issues such as cold start, sparsity, and computational complexity in recommendation systems. The method integrates time and feature information into the optimization model, demonstrating improved efficiency and effectiveness compared to state-of-the-art algorithms.
APPLIED SOFT COMPUTING
(2021)
Article
Mechanics
M. Abbasi, A. H. Namadchi, J. Alamatian
Summary: This research introduces a new algorithm for the Dynamic Relaxation (DR) method using Lagrangian interpolation functions to calculate nodal displacement. The power iteration method is used to determine the optimal time step ratio, eliminating the need for the restarting analysis phase. Analysis of structures with geometrically nonlinear behavior shows that the new kinetic DR scheme reduces the number of convergence iterations and analysis duration compared to conventional DR methods.
MECHANICS BASED DESIGN OF STRUCTURES AND MACHINES
(2023)
Article
Computer Science, Information Systems
Jia Tang
Summary: This paper proposes a fractional stochastic gradient algorithm for handling nonlinear systems with piece-wise linear input, and introduces a multi-innovation fractional stochastic gradient algorithm to improve the convergence rate.
Article
Operations Research & Management Science
Joao Carlos de O. Souza, Joao Xavier da Cruz Neto, Jurandir de Oliveira Lopes, Roberto Cristovao Mesquita Silva, Sandro Dimy Barbosa Bitar
Summary: This paper presents a method for solving constrained multiobjective problems with a vector-valued DC objective function. The method extends both the scalar and vectorial proximal point methods by introducing a vectorial regularization function, offering additional flexibility. Encouraging numerical experiments are presented to validate the method's feasibility.
Article
Computer Science, Artificial Intelligence
Muhammad Shahkar Khan, Haider Ali, Muhammad Zakarya, Santosh Tirunagari, Ayaz Ali Khan, Rahim Khan, Aftab Ahmed, Lavdie Rada
Summary: In this article, a novel variational model is proposed for concurrent restoration and segmentation of noisy images with intensity inhomogeneity and high contrast background illumination. The model combines multi-phase segmentation technology with a statistical approach to enable inhomogeneous image restoration. Through tests and simulations, the proposed model is shown to outperform cutting-edge two-phase and multi-phase methods in accurately segmenting images with noise, background light, and inhomogeneity.
Article
Engineering, Multidisciplinary
Jyoti Gupta, Ashish Goel
Summary: In this paper, a novel exponential-based approximation for the Gaussian Q-function is proposed and compared with existing methods. The proposed approximation is shown to be accurate and outperform existing methods. It is applied to evaluate the symbol error probability of TQAM schemes under various channel conditions and validated through Monte Carlo simulations.
SADHANA-ACADEMY PROCEEDINGS IN ENGINEERING SCIENCES
(2022)
Article
Mathematics, Applied
Arnesh Sujanani, Renato D. C. Monteiro
Summary: This work presents an adaptive superfast proximal augmented Lagrangian method for solving nonconvex composite optimization problems. The method is advantageous in that it requires no prior knowledge of the optimization problem parameters and demonstrates excellent speed and efficiency.
JOURNAL OF SCIENTIFIC COMPUTING
(2023)
Article
Engineering, Multidisciplinary
Yiguo Chen, Congjun Feng, Yonghong He, Zhijun Chen, Xiaowei Fan, Chao Wang, Xinmin Ge
Summary: This paper proposes a novel inversion algorithm using empirical truncated singular value decompositions (TSVD) and the linearized Bregman iteration to accelerate convergence and enhance precision. The L1 penalty term is applied to construct the objective function, and the linearized Bregman iteration is utilized for fast convergence. Numerical simulations validate the efficiency of this novel inversion method, achieving quick and effective data solutions with low signal-to-noise ratios.
CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES
(2023)
Article
Engineering, Chemical
Hasan Sildir, Erdal Aydin
Summary: This study introduces a piecewise-linear approximation method for handling non-convex activation and objective functions in artificial neural networks, achieving optimal, global, and simultaneous training and feature selection in regression problems, with efficient approximations and significant improvement in test accuracy.
CHEMICAL ENGINEERING SCIENCE
(2022)
Article
Computer Science, Software Engineering
Yanli Liu, Ernest K. Ryu, Wotao Yin
MATHEMATICAL PROGRAMMING
(2019)
Article
Operations Research & Management Science
Tao Sun, Yuejiao Sun, Yangyang Xu, Wotao Yin
COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
(2020)
Article
Computer Science, Artificial Intelligence
Chun-Na Li, Yuan-Hai Shao, Wotao Yin, Ming-Zeng Liu
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
(2020)
Article
Mathematics, Applied
Xinmeng Huang, Ernest K. Rya, Wotao Yin
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2020)
Article
Mathematics, Applied
Jialin Liu, Wotao Yin, Wuchen Li, Yat Tin Chow
Summary: The paper proposes a fast algorithm for calculating the Wasserstein-1 distance, based on multilevel primal-dual algorithms, and demonstrates its computational speed through numerical examples and complexity analysis. The proposed algorithm provides solutions within 0.2 to 1.5 seconds on a single CPU for commonly used image examples of size 512 x 512, which is much faster than state-of-the-art algorithms.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2021)
Article
Computer Science, Software Engineering
Ernest K. Ryu, Robert Hannah, Wotao Yin
Summary: This paper introduces a geometric approach to analyzing the convergence of fixed point iterations by utilizing a new tool called the scaled relative graph. This tool establishes a correspondence between nonlinear operators and subsets of the 2D plane, allowing for a rigorous proof of convergence through geometric arguments in the 2D plane.
MATHEMATICAL PROGRAMMING
(2022)
Article
Mathematics, Applied
Yiyang Liu, Zaiwen Wen, Wotao Yin
Summary: The goal of this paper is to efficiently solve the large-scale linear programming formulation of Optimal Transport problems. The key observations are the sparsity of primal solutions and the good geometric properties of the cost function. Based on these observations, the paper proposes an algorithm that utilizes a hierarchical multiscale structure to solve large-scale OT problems and significantly improve efficiency in the computation process.
JOURNAL OF SCIENTIFIC COMPUTING
(2022)
Article
Mathematics, Applied
Jinshan Zeng, Wotao Yin, Ding-Xuan Zhou
Summary: The augmented Lagrangian method (ALM) is a useful method for constrained optimization, but it can experience oscillations and divergence when the underlying problem is nonconvex and nonsmooth. This paper modifies ALM to use a Moreau envelope and establishes its convergence. Two practical variants are also proposed.
JOURNAL OF SCIENTIFIC COMPUTING
(2022)
Article
Mathematics, Applied
Howard Heaton, Samy Wu Fung, Alex Tong Lin, Stanley Osher, Wotao Yin
Summary: Inverse problems are important in recovering signals from noisy measurements. This study proposes a new algorithm called Wasserstein-based projection (WP) that approximates the true projection with high probability, providing theoretical guarantees for optimization methods in signal recovery.
SIAM JOURNAL ON MATHEMATICS OF DATA SCIENCE
(2022)
Article
Engineering, Electrical & Electronic
Tianyi Chen, Yuejiao Sun, Wotao Yin
Summary: Stochastic compositional optimization generalizes classic stochastic optimization for minimizing compositions of functions, with applications in reinforcement learning and meta learning. The new Stochastically Corrected Stochastic Compositional gradient method (SCSC) ensures convergence at the same rate as traditional methods and can be accelerated with SGD techniques. Applying Adam to SCSC achieves state-of-the-art performance in stochastic compositional optimization, tested in model-agnostic meta-learning tasks.
IEEE TRANSACTIONS ON SIGNAL PROCESSING
(2021)
Article
Engineering, Electrical & Electronic
Tianyi Chen, Yuejiao Sun, Wotao Yin
Summary: The algorithm LASG is developed to solve distributed learning problems efficiently, saving communication costs and tailored for stochastic gradients. Through introducing new rules and analysis, LASG achieves impressive empirical performance in practice.
IEEE TRANSACTIONS ON SIGNAL PROCESSING
(2021)
Article
Engineering, Electrical & Electronic
Huan Li, Cong Fang, Wotao Yin, Zhouchen Lin
IEEE TRANSACTIONS ON SIGNAL PROCESSING
(2020)
Article
Engineering, Electrical & Electronic
Xinwei Zhang, Mingyi Hong, Sairaj Dhople, Wotao Yin, Yang Liu
Summary: This paper studies the behavior of the FedAvg algorithm in Federated Learning (FL) and proposes a new algorithm design strategy to design FL algorithms that are fast and require minimal assumptions, achieving optimal optimization and communication complexity, accommodating various local computation models. The new algorithms are communication efficient, with communication effort reducing as the heterogeneity among local data decreases.
IEEE TRANSACTIONS ON SIGNAL PROCESSING
(2021)
Article
Engineering, Electrical & Electronic
Yanli Liu, Yuejiao Sun, Wotao Yin
Summary: This paper develops new algorithms for decentralized machine learning over a network to reduce computation and communication complexities by running warm-started Katyusha algorithm. Experimental results demonstrate that these algorithms can significantly reduce computational and communication costs compared to state-of-the-art techniques.
IEEE TRANSACTIONS ON SIGNAL PROCESSING
(2021)
Article
Engineering, Electrical & Electronic
Xianghui Mao, Kun Yuan, Yubin Hu, Yuantao Gu, Ali H. Sayed, Wotao Yin
IEEE TRANSACTIONS ON SIGNAL PROCESSING
(2020)