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NUMERICAL ANALYSIS OF THE PARALLEL ORBITAL-UPDATING APPROACH FOR EIGENVALUE PROBLEMS∗

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arXiv 2024年

作者： Dai, Xiaoying Li, Yan Yang, Bin Zhou, Aihui LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China School of Statistics and Mathematics Central University of Finance and Economics Beijing102206 China

The parallel orbital-updating approach is an orbital/eigenfunction iteration based approach for solving eigenvalue problems when many eigenpairs are required. It has been proven to be efficient, for instance, in electronic structure calculations. In this paper, based on the investigation of a quasi-orthogonality, we present the numerical analysis of the parallel orbital-updating approach for linear eigenvalue problems, including convergence and error estimates of the numerical approximations. Copyright © 2024, The Authors. All rights reserved.

关键词： Eigenvalues and eigenfunctions

QoS-based Beamforming and Compression Design for Cooperative Cellular Networks via Lagrangian Duality

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arXiv 2023年

作者： Fan, Xilai Liu, Ya-Feng Liu, Liang Chang, Tsung-Hui State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China Department of Electronic and Information Engineering The Hong Kong Polytechnic University Hong Kong School of Science and Engineering The Chinese University of Hong Kong Shenzhen Research Institute of Big Data Shenzhen Shenzhen China

This paper considers the quality-of-service (QoS)based joint beamforming and compression design problem in the downlink cooperative cellular network, where multiple relay-like base stations (BSs), connected to the central processor via rate-limited fronthaul links, cooperatively transmit messages to the users. The problem of interest is formulated as the minimization of the total transmit power of the BSs, subject to all users’ signal-to-interference-plus-noise ratio (SINR) constraints and all BSs’ fronthaul rate constraints. In this paper, we first show that there is no duality gap between the considered joint optimization problem and its Lagrangian dual by showing the tightness of its semidefinite relaxation (SDR). Then, we propose an efficient algorithm based on the above duality result for solving the considered problem. The proposed algorithm judiciously exploits the special structure of an enhanced Karush-Kuhn-Tucker (KKT) conditions of the considered problem and finds the solution that satisfies the enhanced KKT conditions via two fixed point iterations. Two key features of the proposed algorithm are: (1) it is able to detect whether the considered problem is feasible or not and find its globally optimal solution when it is feasible;(2) it is highly efficient because both of the fixed point iterations in the proposed algorithm are linearly convergent and evaluating the functions in the fixed point iterations are computationally cheap. Numerical results show the global optimality and efficiency of the proposed algorithm. Copyright © 2023, The Authors. All rights reserved.

关键词： Quality of service

A Dynamic Pyramidal Relaxation Method of AC OPF

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A Dynamic Pyramidal Relaxation Method of AC OPF

Power and Electrical engineering (ACPEE), 5th Asia Conference on

作者： Yu-Yang Tang Liang Chen Hongbo Du Sheng-Jie Chen Caixia Kou Xiaomeng Ai Bo Zhou Academy of Mathematics and Systems Science Chinese Academy of Sciences Institute of Computational Mathematics and Scientific/Engineering Computing Beijing China College of Sciences Beijing University of Posts and Telecommunications Beijing China Academy of Mathematics and Systems Science Chinese Academy of Sciences Institute of Applied Mathematics Beijing China School of Electrical and Electronic Engineering Huazhong University of Science and Technology Wuhan China Department of Industrial and Operations Engineering University of Michigan Ann Arbor United States

ISBN: (数字)9798350309638

ISBN: (纸本)9798350309645

The Alternating Current Optimal Power Flow (AC OPF) is crucial for power system analysis, yet existing algorithms face challenges in meeting the diverse requirements of practical applications. This paper presents a Pyramidal Relaxation (PR) formulation of the Branch Flow Model (BFM) for AC OPF, where surface conical constraints are approximated through a union of tetrahedrons in a Mixed Integer Linear Programming (MILP) relaxation. To reduce problem size and to enhance computational efficiency, we proposed a Dynamic Pyramidal Relaxation (DPR) method, where the cuts (inner approximation and outer approximation) are adaptively added. In practice, the DPR method is embedded into a MILP commercial solver based on the branch-and-cut framework. Case studies in different test systems validate the effectiveness in terms of feasibility, accuracy, and efficiency of our proposed method.

关键词： Electrical engineering computational modeling Power system dynamics Asia Linear approximation Relaxation methods Mixed integer linear programming

FINITE CONVERGENCE OF MOMENT-SOS RELAXATIONS WITH NON-REAL RADICAL IDEALS

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arXiv 2023年

作者： Huang, Lei Nie, Jiawang Yuan, Ya-Xiang Department of Mathematics University of California 9500 Gilman Drive La Jolla San DiegoCA92093 United States Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100049 China

We consider the linear conic optimization problem with the cone of nonnegative polynomials. Its dual optimization problem is the generalized moment problem. Moment-SOS relaxations are powerful for solving them. This paper studies finite convergence of the Moment-SOS hierarchy when the constraining set is defined by equations whose ideal may not be real radical. Under the archimedeanness, we show that the Moment-SOS hierarchy has finite convergence if some classical optimality conditions hold at every minimizer of the optimal nonnegative polynomial for the linear conic optimization problem. When the archimedeanness fails (this is the case for unbounded sets), we propose a homogenized Moment-SOS hierarchy and prove its finite convergence under similar assumptions. Furthermore, we also prove the finite convergence of the Moment-SOS hierarchy with denominators. In particular, this paper resolves a conjecture posed in the earlier work. Copyright © 2023, The Authors. All rights reserved.

关键词： Polynomials

Understanding Comparative Genomics Data Visualization for Biodiversity Domain Through Persona-Based Interviews

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Understanding Comparative Genomics Data Visualization for Bi...

2024 IEEE International Conference on computing, ICOCO 2024

作者： Chan, Vei Siang Mohamed, Farhan Bin Salleh, Faezah Binti Mohd Iglesias, Andres Jamaludin, Najwa Ayuni Binti Mustafa Albakri, Ikmal Faiq Albakri Media and Game Innovation Center of Excellence Institute of Human Centered Engineering Universiti Teknologi Malaysia Johor Bahru Malaysia Department of Biosciences Faculty of Science Universiti Teknologi Malaysia Johor Bahru Malaysia Department of Applied Mathematics and Computational Sciences Universidad de Cantabria Santander Spain Pervasive Computing & Educational Technology Department of Media Interactive Fakulti Teknologi Maklumat dan Komunikasi Universiti Teknikal Malaysia Melaka Melaka Malaysia

ISBN: (纸本)9798331530303

Understanding the needs of genomic data visualization techniques is important to help bioinformaticians to perform their comparative analytical tasks effectively. DNA sequencing datasets consist of a long sequential string of nucleotide base pairs combination and are often involved in multiple sequences alignment for comparative analysis. Therefore, existing challenges include designing suitable visualization layout and the need of user-centered approach to ensure optimal user experience. Existing works also featured heavily on the qualitative evaluation of comparative visualization tools, such as use cases and case studies, which are difficult to quantify and conduct follow up evaluation for tool improvement. Hence, this paper aims to understand the needs of visualization tools in comparative genomic analysis to identify visualization tasks and visual design requirements. The methodology includes the creation of semi-structured interview based on personas template as guiding questions and the synthesis of thematic analysis results. These results presented the requirements of the visualization tasks for the biodiversity domain based on comparative targets. For future work, this research will design, develop, and validate the comparative visualization tool based on the discovered requirements. ©2024 IEEE.

关键词： Genome

A Mathematical Aspect of Bloch's Theorem

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arXiv 2024年

作者： Li, Yan Yang, Bin Zhou, Aihui LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China NCMIS Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

In this paper, by studying a class of 1-D Sturm-Liouville problems with periodic coefficients, we show and classify the solutions of periodic Schrodinger equations in a multidimensional case, which tells that not all the solutions are Bloch solutions. In addition, we also provide several properties of the solutions and quasimomenta and illustrate the relationship between bounded solutions and Bloch solutions. Copyright © 2024, The Authors. All rights reserved.

关键词：

Cross-Platform Multimodal Frogeye Leaf Spot Recognition and Classification: Advancing with Cutting-Edge CNN Technologies and Transfer Learning in Diverse Plant Species 7

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Cross-Platform Multimodal Frogeye Leaf Spot Recognition and ...

7th International Conference on Circuit Power and computing Technologies, ICCPCT 2024

作者： Mohan, G. Usharani, R. Tomar, Vatsala Arthi, A. Kuriyal, Suniti Kumar Yuvaraj, K.P. K.S.Rangasamy College of Technology Department of Mathematics Tamil Nadu India SRM Institute of Science and Technology School of Computing Department of Computational Intelligence Faculty of Engineering and Technology Chennai India IIMT University School of Life Science & Technology Department of Botany UP Meerut India Karpagam College of Engineering Department of Information Technology Coimbatore India Pt.L.M.S.Sridev Suman Uttarakhand University Campus Department of Botany Rishikesh India Sri Krishna College of Engineering and Technology Department of Mechanical Engineering Coimbatore India

ISBN: (纸本)9798350372816

Frogeye Leaf Spot, a common agricultural disease, poses a significant threat to crop yields. Using multimodal data from different platforms successfully has been a hurdle for existing research in leaf spot detection. Using cutting-edge convolutional neural network (CNN) and transfer learning techniques, this research presents a Cross-Platform Multimodal Recognition system to solve this issue. With a recall of 0.88, F1-score of 0.90, accuracy of 0.91, and precision of 0.92, the suggested method demonstrates exceptional performance. Our accuracy is 6% higher, F1-score is 8% higher, and recall is 9% higher than the preceding state-of-the-art, according to comparisons with previous studies. Improved Frogeye Leaf Spot detection on many platforms is a direct result of our method's success in combining picture and sensor data. This study improves farmers' ability to identify diseases and provides a solid answer for precision agriculture. Our Cross-Platform Multimodal Recognition system has shown to be effective in enhancing agricultural disease recognition, and the shown advances highlight its potential influence on crop management tactics. © 2024 IEEE.

关键词： Convolutional neural networks

A new framework of high-order unfitted finite element methods using ALE maps for moving-domain problems

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arXiv 2024年

作者： Lu, Wenhao Ma, Chuwen Zheng, Weiying LSEC NCMIS Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematical Science University of Chinese Academy of Sciences Beijing100049 China Institute of Natural Sciences Shanghai Jiao Tong University Shanghai200240 China

As a sequel to our previous work [C. Ma, Q. Zhang and W. Zheng, SIAM J. Numer. Anal., 60 (2022)], [C. Ma and W. Zheng, J. Comput. Phys. 469 (2022)], this paper presents a generic framework of arbitrary Lagrangian-Eulerian unfitted finite element (ALE-UFE) methods for partial differential equations (PDEs) on time-varying domains. The ALE-UFE method has a great potential in developing high-order unfitted finite element methods. The usefulness of the method is demonstrated by a variety of moving-domain problems, including a linear problem with explicit velocity of the boundary (or interface), a PDE-domain coupled problem, and a problem whose domain has a topological change. Numerical experiments show that optimal convergence is achieved by both third- and fourth-order methods on domains with smooth boundaries, but is deteriorated to the second order when the domain has topological changes. Copyright © 2024, The Authors. All rights reserved.

关键词： Finite element method

A New Adaptive Balanced Augmented Lagrangian Method with Application to ISAC Beamforming Design

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arXiv 2024年

作者： Wu, Jiageng Jiang, Bo Li, Xinxin Liu, Ya-Feng Yuan, Jianhua School of Mathematics Jilin University Changchun130012 China Ministry of Education Key Laboratory for NSLSCS School of Mathematical Sciences Nanjing Normal University Nanjing210023 China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Sciences Beijing University of Posts and Telecommunications Beijing100876 China

In this paper, we consider a class of convex programming problems with linear equality constraints, which finds broad applications in machine learning and signal processing. We propose a new adaptive balanced augmented Lagrangian (ABAL) method for solving these problems. The proposed ABAL method adaptively selects the stepsize parameter and enjoys a low per-iteration complexity, involving only the computation of a proximal mapping of the objective function and the solution of a linear equation. These features make the proposed method wellsuited to large-scale problems. We then custom-apply the ABAL method to solve the ISAC beamforming design problem, which is formulated as a nonlinear semidefinite program in a previous work. This customized application requires careful exploitation of the problem's special structure such as the property that all of its signal-to-interference-and-noise-ratio (SINR) constraints hold with equality at the solution and an efficient computation of the proximal mapping of the objective function. Simulation results demonstrate the efficiency of the proposed ABAL method. © 2024, CC BY.

关键词： Signal to noise ratio