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Novel efficient iterative schemes for linear finite element approximations of elliptic optimal control problems with integral constraint on the state

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2025年 456卷

作者： Ge, Liang Huang, Jian Zhou, Jianwei Univ Jinan Sch Math Sci Jinan 250022 Peoples R China Xiangtan Univ Sch Math & Computat Sci Xiangtan Hunan Peoples R China Natl Ctr Appl Math Hunan Xiangtan 411105 Peoples R China Linyi Univ Sch Math & Stat Linyi 276000 Peoples R China

Centering on a distributed optimal control problem governed by elliptic equations with a unilateral integral constraint on the state, we recall the first-order optimality conditions to explore variational formulations. The classical linear finite element method is employed to approximate the equivalent formulae. Taking into account the distinctive structural characteristics of discretized schemes, we divide the discretized optimal conditions into two equivalent matrix schemes. Subsequently, we introduce an efficient iterative algorithm designed to solve the approximation schemes. We demonstrate the convergence of our iterative algorithm and investigate its robustness and uniform optimality under a specified constraint, particularly focusing on small regularization parameters. Finally, numerical tests are conducted using various h and alpha to illustrate the efficiency of our proposed algorithm. These tests also validate a tremendous reduction in the number of required iterations.

关键词： Distributed optimal control problem Unilateral integral state-constraint Finite element method efficient algorithm Robustness

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An efficient generic direct integration method for the generalized damping structure dynamic system

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MECHANICAL SYSTEMS AND SIGNAL PROCESSING 2025年 224卷

作者： Shen, Renjie Liu, Junjie Xu, Lixin Jiangsu Univ Sci & Technol Sch Naval Architecture & Ocean Engn Dept Engn Mech Zhenjiang Peoples R China Jiangsu Univ Sci & Technol Ocean Coll Zhenjiang Peoples R China Jiangsu Marine Technol Innovat Ctr Nantong Peoples R China

Generalized damping is a time-memory nonlocal model that takes the complete history velocity into account through a convolution. The kernel function of the convolution represents the distribution or the weight of history velocity in the time dimension. In this work, a high-efficiency algorithm is proposed for the calculation of generalized damping convolution. In this algorithm, the kernel function in the convolution is approximated by Fourier series. The relationship between the second derivative of the convolution and the convolution itself has been established. The derivative of the convolution is computed through multi-points difference scheme. This algorithm combined with direct time integration method is a generic method that can be applied for any causal kernel functions. By analyzing the computational complexity of different methods, it can be seen that the computational complexity of the existing methods is not only related to the number of degrees of freedom of the system, but also has a quadratic or cubic relationship with the number of computational steps. The computational efficiency of the proposed method is only related to the number of degrees of freedom of the system, not the number of steps, its efficiency is higher than that of the existing direct integration methods. Numerical examples are provided to illustrate the accuracy and especially the efficiency of the integration.

关键词： Direct integration method Generalized damping efficient algorithm Kernel function

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efficient online sensitivity analysis for the injective bottleneck path problem

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OPTIMIZATION LETTERS 2024年 1-14页

作者： Kaymakov, Kirill V. Malyshev, Dmitry S. Coleman Tech LLC 40 Mira Ave Moscow 129090 Russia Natl Res Univ Higher Sch Econ Lab Algorithms & Technol Networks Anal 136 Rodionova Str Nizhnii Novgorod 603093 Russia

The tolerance of an element of a combinatorial optimization problem with respect to a given optimal solution is the maximum change, i.e., decrease or increase, of its cost, such that this solution remains optimal. The bottleneck path problem, for given an edge-capacitated graph, a source, and a target, is to find the max\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\max $$\end{document}-min\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\min $$\end{document} value of edge capacities on paths between the source and the target. For any given sample of this problem with n vertices and m edges, there is known the Ramaswamy-Orlin-Chakravarty's algorithm to compute an optimal path and all tolerances with respect to it in O(m+nlogn)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O(m+n\log n)$$\end{document} time. In this note, for any in advance given (n, m)-network with distinct edge capacities and k source-target pairs, we propose an O(m alpha(m,n)+min((n+k)logn,km))\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O\Big (m \alpha (m,n)+\min \big ((n+k)\log n,km\big )\Big )$$\end{document}-time preprocessing, where alpha(,)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssym

关键词： Bottleneck path problem Sensitivity analysis efficient algorithm

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An efficient approach for discovering Graph Entity Dependencies (GEDs)

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INFORMATION SYSTEMS 2024年 125卷

作者： Liu, Dehua Kwashie, Selasi Zhang, Yidi Zhou, Guangtong Bewong, Michael Wu, Xiaoying Guo, Xi He, Keqing Feng, Zaiwen Huazhong Agr Univ Coll Informat Wuhan Hubei Peoples R China Charles Sturt Univ AI & Cyber Futures Inst Bathurst NSW Australia Charles Sturt Univ Sch Comp & Math Wagga Wagga NSW Australia Wuhan Univ Sch Comp Wuhan Hubei Peoples R China

Graph entity dependencies (GEDs) are novel graph constraints, unifying keys and functional dependencies, for property graphs. They have been found useful in many real-world data quality and data management tasks, including fact checking on social media networks and entity resolution. In this paper, we study the discovery problem of GEDs-finding a minimal cover of valid GEDs in a given graph data. We formalise the problem, and propose an effective and efficient approach to overcome major bottlenecks in GED discovery. In particular, we leverage existing graph partitioning algorithms to enable fast GED-scope discovery, and employ effective pruning strategies over the prohibitively large space of candidate dependencies. Furthermore, we define an interestingness measure for GEDs based on the minimum description length principle, to score and rank the mined cover set of GEDs. Finally, we demonstrate the scalability and effectiveness of our GED discovery approach through extensive experiments on real-world benchmark graph data sets;and present the usefulness of the discovered rules in different downstream data quality management applications.

关键词： Graph entity dependencies Graph entity dependency discovery efficient algorithm Data dependencies

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MMBypass: Towards efficient multi-modal AI computing with adaptive bypass network

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JOURNAL OF PARALLEL AND DISTRIBUTED COMPUTING 2025年 201卷

作者： Pu, Yifei Xia, Xinfeng Hou, Xiaofeng Wang, Chi Xu, Cheng Liu, Jiacheng Wang, Jing Guo, Minyi Yuan, Jingling Li, Chao Shanghai Jiao Tong Univ Comp Sci & Engn Shanghai Peoples R China Chinese Univ Hong Kong Comp Sci & Engn Hong Kong Peoples R China Wuhan Univ Technol Hubei Key Lab Transportat Internet Things Wuhan Peoples R China

Multi-modal artificial intelligence systems demonstrate superior performance through cross-modal information fusion and processing mechanisms, surpassing conventional unimodal architectures. However, the enhanced computational complexity required for processing heterogeneous data streams in multi-modal frameworks results in elevated inference latency compared to their uni-modal architectures. This limitation significantly constrains deployment feasibility for real-time and large-scale applications. To address this challenge, we present MMBypass, an adaptive and efficient architecture for multi-modal AI acceleration. Our solution implements intelligent layer-skipping mechanisms through adaptive computational complexity analysis of multi-modal tasks, achieving latency reduction while maintaining predictive accuracy and mitigating model overfitting in specialized scenarios. The architecture's innovation lies in two aspects: 1) We design bypasses for each uni-modal network in multi-modal networks to perform adaptive computing. 2) We design a guider to dynamically choose the optimal bypasses. Distinct from existing methods, MMBypass maintains broad applicability without requiring domain-specific prerequisites, and it shows significantly better performance on data samples with different difficulties. Empirical evaluations demonstrate our architecture achieves 44.5% average latency reduction while matching or exceeding baseline accuracy across diverse multi-modal benchmarks.

关键词： Multi-modal artificial intelligence DNN optimization efficient algorithm Adaptive learning

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Computational efficient Approximations of the Concordance Probability in a Big Data Setting

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BIG DATA 2024年第3期12卷 243-268页

作者： Van Oirbeek, Robin Ponnet, Jolien Baesens, Bart Verdonck, Tim Allianz Benelux Data Off Brussels Belgium Katholieke Univ Leuven Fac Sci Dept Math Leuven Belgium Katholieke Univ Leuven Fac Econ & Business Leuven Belgium Univ Southampton Sch Management Southampton England UAntwerp imec Fac Sci Dept Math Antwerp Belgium Katholieke Univ Leuven Fac Econ & Business B-3000 Leuven Belgium

Performance measurement is an essential task once a statistical model is created. The area under the receiving operating characteristics curve (AUC) is the most popular measure for evaluating the quality of a binary classifier. In this case, the AUC is equal to the concordance probability, a frequently used measure to evaluate the discriminatory power of the model. Contrary to AUC, the concordance probability can also be extended to the situation with a continuous response variable. Due to the staggering size of data sets nowadays, determining this discriminatory measure requires a tremendous amount of costly computations and is hence immensely time consuming, certainly in case of a continuous response variable. Therefore, we propose two estimation methods that calculate the concordance probability in a fast and accurate way and that can be applied to both the discrete and continuous setting. Extensive simulation studies show the excellent performance and fast computing times of both estimators. Finally, experiments on two real-life data sets confirm the conclusions of the artificial simulations.

关键词： AUC C-index clustering efficient algorithm performance measure

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An efficient algorithm for linear semi-infinite programming over positive polynomials

An efficient algorithm for linear semi-infinite programming ...

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12th International Symposium on Operations Research and its Applications in Engineering, Technology and Management (ISORA 2015)

作者： Meiling Xu Zongwei Luo South University of Science and Technology China

This paper describes an efficient implementation of a form of linear semi-infinite programming (LSIP). We look at maximizing (minimizing) a linear function over a set of constraints formed by positive trigonometric polynomials. Previous studies about LSIP are formulated using semi-definite programming (SDP), this is typically done by using the Kalman Yakubovich Popov (KYP) lemma or using a trace operation involving a Grammian matrix, which can be computationally expensive. The proposed algorithm is based on simplex method that directly solves the LSIP without any parameterization. Numerical results show that the proposed LISP algorithm is significantly more efficient than existing SDP solvers using KYP lemma and Grammian matrix, in both execution time and memory.

关键词： Linear semi-infinite programming positive trigonometric polynomials. semi-definite programming simplex method Simplex method efficient algorithm Programming Polynomial Service Discovery Protocol Lemma linear function execution time

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On efficient Parameter Estimation of Elementary Chirp Model

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2023年 71卷 2352-2365页

作者： Mittal, Anjali Grover, Rhythm Kundu, Debasis Mitra, Amit Indian Inst Technol Kanpur Dept Math & Stat Kanpur 208016 India Indian Inst Technol Guwahati Sch Data Sci & Artificial Intelligence Gauhati 781039 India

Elementary chirp signals can be found in various fields of science and engineering. We propose two computationally efficient algorithms based on the choice of two different initial estimators to estimate the parameters of the elementary chirp model. It is observed that the proposed efficient estimators are consistent;they have the identical asymptotic distribution as that of the least squares estimators and they are also less computationally intensive. We also propose sequential efficient procedures to estimate the parameters of the multi-component elementary chirp model. The asymptotic properties of the sequential efficient estimators coincide with the least squares estimators. The important point about the efficient and sequential efficient algorithms is that these algorithms produce efficient frequency rate estimators in a fixed number of iterations. Another important point is that the under normal error assumption the theoretical variances of the proposed estimators achieve the Cramer-Rao lower bounds asymptotically. Simulation experiments are performed to see the performance of the proposed estimators, and it is observed that they are computationally efficient, take less time in computation than the other existing methods and perform well when two frequency rates are close to each other upto a reasonably low degree of separation. On an EEG dataset, we demonstrate the performance of the proposed algorithm.

关键词： Elementary chirp efficient algorithm least squares sequential efficient algorithm frequency rate consistency asymptotic normality

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A novel algorithm and software for 3D density gravity inversion

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COMPUTERS & GEOSCIENCES 2025年 196卷

作者： Chen, Wenjin Tan, Xiaolong Liu, Yang Jiangxi Univ Sci & Technol Sch Civil & Surveying & Mapping Engn Ganzhou Peoples R China Jiangxi Univ Sci & Technol Jiangxi Prov Key Lab Water Ecol Conservat Headwate 1958 Ke-Jia Rd Ganzhou Peoples R China Jiangxi Sci & Technol Normal Univ Foreign Language Sch Ganzhou Peoples R China

In this study, we present a novel algorithm for three-dimensional density gravity inversion in the spectral domain. By applying the Fast Fourier Transform (FFT) to the observation equation and introducing an auxiliary function, we establish a general functional relationship between gravity anomalies and density. To address the ill-posed nature of the three-dimensional density inversion problem, we propose a new auxiliary function with two multiplicative factors: one to adjust density variation with depth and another to reflect the solution characteristics. Additionally, we have developed a user-friendly software interface using the scientific computing language Matlab. Both synthetic and field data are used to validate the proposed algorithm and software. Noise tests are conducted to demonstrate the efficacy and robustness of the proposed method. A comparative analysis with the smoothing and focusing methods is also performed. The results show that the proposed method outperforms the smoothing method and achieves higher resolution, although it is smoother than the focusing inversion results. Furthermore, we compare the computational times of the three methods, and the results indicate that the proposed method is the most efficient.

关键词： 3D density inversion efficient algorithm Spectral domain Software

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Advanced Computational-Time Reduction Technology of Nonlinear Fourier-Based and Magnetic Circuit Hybrid Model

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IEEE TRANSACTIONS ON TRANSPORTATION ELECTRIFICATION 2025年第1期11卷 3617-3630页

作者： Li, Jingze Wu, Lijian Wu, Xinzhen Zhejiang Univ Coll Elect Engn Hangzhou 310027 Peoples R China Qingdao Univ Coll Elect Engn Qingdao 266071 Peoples R China

Given the rising demand in modern industry for high-performance permanent magnet (PM) machines and advanced control strategies, more efficient computation tools are an urgent necessity. To address nonlinear characteristics like magnetic saturation in PM machines, hybrid models (HMs) have seen rapid development in recent years. Among these, the nonlinear Fourier-based and magnetic circuit (MC) HMs offer advantages of high accuracy and clear physical significance. However, both the high-dimensional stiffness matrix in the Fourier model and tedious iteration process in the nonlinear MC model contribute to CPU usage issues and unacceptably time consumption. To cope with these issues, the author puts forth a series of efficient techniques aimed at reducing computational burden. These techniques are derived from both individual computations of the two sub-models and iterative calculations between them. They leverage aspects such as PM machine magnetic field distribution, efficient matrix-solving algorithms, nonlinear equation convergence algorithms, and so on. Furthermore, the author outlines tailored capable techniques corresponding to the distinct characteristics of inner and outer rotor structures, as well as surface-mounted and interior PM topologies. Through finite element modeling and prototype experiments, employing these techniques substantially decreases time consumption while maintaining accuracy.

关键词： Computational modeling Mathematical models Topology Integrated circuit modeling Saturation magnetization Rotors Solid modeling Calculation speed efficient algorithm Fourier-based model hybrid model (HM) magnetic circuit (MC) permanent magnet (PM) machines

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