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NONMONOTONE LOCAL MINIMAX METHODS FOR FINDING MULTIPLE SADDLE POINTS

Journal of Computational Mathematics 2024年第3期42卷 851-884页

作者： Wei Liu Ziqing Xie Wenfan Yi South China Research center for Applied Mathematics and Interdisciplinary Studies South China Normal UniversityGuangzhou 510631China Key Laboratory of Computing and stochastic Mathematics(Ministry of Education) Hunan Normal UniversityChangshaHunan 410081China Hunan Provincial Key Laboratory of Intelligent Information Processing and Applied Mathematics School of MathematicsHunan UniversityChangshaHunan 410082China

In this paper,by designing a normalized nonmonotone search strategy with the BarzilaiBorwein-type step-size,a novel local minimax method(LMM),which is a globally convergent iterative method,is proposed and analyzed to find multiple(unstable)saddle points of nonconvex functionals in Hilbert *** to traditional LMMs with monotone search strategies,this approach,which does not require strict decrease of the objective functional value at each iterative step,is observed to converge faster with less ***,based on a normalized iterative scheme coupled with a local peak selection that pulls the iterative point back onto the solution submanifold,by generalizing the Zhang-Hager(ZH)search strategy in the optimization theory to the LMM framework,a kind of normalized ZH-type nonmonotone step-size search strategy is introduced,and then a novel nonmonotone LMM is *** feasibility and global convergence results are rigorously carried out under the relaxation of the monotonicity for the functional at the iterative ***,in order to speed up the convergence of the nonmonotone LMM,a globally convergent Barzilai-Borwein-type LMM(GBBLMM)is presented by explicitly constructing the Barzilai-Borwein-type step-size as a trial step-size of the normalized ZH-type nonmonotone step-size search strategy in each ***,the GBBLMM algorithm is implemented to find multiple unstable solutions of two classes of semilinear elliptic boundary value problems with variational structures:one is the semilinear elliptic equations with the homogeneous Dirichlet boundary condition and another is the linear elliptic equations with semilinear Neumann boundary *** numerical results indicate that our approach is very effective and speeds up the LMMs significantly.

关键词： Multiple saddle points Local minimax method Barzilai-Borwein gradient method Normalized nonmonotone search strategy Global convergence

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Efficient slope reliability analysis under soil spatial variability using maximum entropy distribution with fractional moments

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Journal of Rock Mechanics and Geotechnical Engineering 2024年第4期16卷 1140-1152页

作者： Chengxin Feng Marcos A.Valdebenito Marcin Chwała Kang Liao Matteo Broggi Michael Beer Institute for Risk and Reliability Leibniz University HannoverCallinstr.34Hannover30167Germany Chair for Reliability Engineering TU Dortmund UniversityLeonhard-Euler-Str.5Dortmund44227Germany Faculty of Civil Engineering Wrocƚaw University of Science and TechnologyWrocƚawPoland Faculty of Geosciences and Environmental Engineering Southwest Jiaotong UniversityChengdu610031China University of Liverpool Institute for Risk and UncertaintyPeach StreetLiverpoolL69 7ZFUnited Kingdom International Joint Research center for Resilient Infrastructure & International Joint Research center for Engineering Reliability and stochastic Mechanics Tongji UniversityShanghaiChina

Spatial variability of soil properties imposes a challenge for practical analysis and design in geotechnical *** latter is particularly true for slope stability assessment,where the effects of uncertainty are synthesized in the so-called probability of *** probability quantifies the reliability of a slope and its numerical calculation is usually quite involved from a numerical *** view of this issue,this paper proposes an approach for failure probability assessment based on Latinized partially stratified sampling and maximum entropy distribution with fractional *** spatial variability of geotechnical properties is represented by means of random fields and the Karhunen-Loève ***,failure probabilities are estimated employing maximum entropy distribution with fractional *** application of the proposed approach is examined with two examples:a case study of an undrained slope and a case study of a slope with cross-correlated random fields of strength parameters under a drained *** results show that the proposed approach has excellent accuracy and high efficiency,and it can be applied straightforwardly to similar geotechnical engineering problems.

关键词： Slope Random field Reliability analysis Maximum entropy distribution Latinized partial stratified sampling

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Detection of astrophysical gravitational wave sources by TianQin and LISA

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Science China(Physics,Mechanics & Astronomy) 2024年第5期67卷 123-163页

作者： Alejandro Torres-Orjuela Shun-Jia Huang Zheng-Cheng Liang Shuai Liu Hai-Tian Wang Chang-Qing Ye Yi-Ming Hu Jianwei Mei MOE Key Laboratory of Tian Qin Mission Tian Qin Research Center for Gravitational PhysicsSchool of Physics and AstronomyFrontiers Science Center for Tian QinGravitational Wave Research Center of CNSASun Yat-Sen University(Zhuhai Campus)Zhuhai 519082China Department of Physics The University of Hong KongHong Kong 999077China Kavli Institute for Astronomy and Astrophysics Peking UniversityBeijing100871China

TianQin and LISA are space-based laser interferometer gravitational wave(GW)detectors planned to be launched in the *** detectors will detect low-frequency GWs around 10^(-2)Hz;however,Tian Qin is more sensitive to frequencies above this common sweet-spot while LISA is more sensitive to frequencies below 10^(-2)***,Tian Qin and LISA will be able to detect the same sources but with different accuracy depending on the source and its *** consider some of the most important astrophysical sources—massive black hole binaries,stellar-mass black hole binaries,double white dwarfs,extreme mass ratio inspirals,light and heavy intermediate mass ratio inspirals,as well as the stochastic gravitational background of astrophysical origin—that Tian Qin and LISA will be able to *** each of these sources,we analyze how far they can be detected(detection distance)and how well their parameters can be measured(detection accuracy)using a Fisher Matrix *** compare the results obtained by the three detection scenarios(Tian Qin alone,LISA alone,and joint detection by LISA and Tian Qin)highlighting the gains from joint detection as well as the contribution of Tian Qin and LISA to a combined study of astrophysical *** particular,we consider the different orientations,lifetimes,and duty cycles of the two detectors to explore how they can give a more complete picture when working together.

关键词： wave extreme stochastic

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Detection of Real-Time Distributed Denial-of-Service (DDoS) Attacks on Internet of Things (IoT) Networks Using Machine Learning Algorithms

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Computers, Materials & Continua 2024年第8期80卷 2139-2159页

作者： Zaed Mahdi Nada Abdalhussien Naba Mahmood Rana Zaki Information Technology center University of TechnologyBaghdad00964Iraq Continuous Education center University of TechnologyBaghdad00964Iraq Computer Science Department University of TechnologyBaghdad00964Iraq

The primary concern of modern technology is cyber attacks targeting the Internet of *** it is one of the most widely used networks today and vulnerable to ***-time threats pose with modern cyber attacks that pose a great danger to the Internet of Things(IoT)networks,as devices can be monitored or service isolated from them and affect users in one way or *** Internet of Things networks is an important matter,as it requires the use of modern technologies and methods,and real and up-to-date data to design and train systems to keep pace with the modernity that attackers use to confront these *** of the most common types of attacks against IoT devices is Distributed Denial-of-Service(DDoS)*** paper makes a unique contribution that differs from existing studies,in that we use recent data that contains real traffic and real attacks on IoT *** a hybrid method for selecting relevant features,And also how to choose highly efficient *** gives the model a high ability to detect distributed denial-of-service *** model proposed is based on a two-stage process:selecting essential features and constructing a detection model using the K-neighbors algorithm with two classifier algorithms logistic regression and stochastic Gradient Descent classifier(SGD),combining these classifiers through ensemble machine learning(stacking),and optimizing parameters through Grid Search-CV to enhance system *** were conducted to evaluate the effectiveness of the proposed model using the CIC-IoT2023 and CIC-DDoS2019 *** evaluation demonstrated the potential of our model in robust intrusion detection in IoT networks,achieving an accuracy of 99.965%and a detection time of 0.20 s for the CIC-IoT2023 dataset,and 99.968%accuracy with a detection time of 0.23 s for the CIC-DDoS 2019 ***,a comparative analysis with recent related works highlighted the superiority of our methodology in in

关键词： DDoS Service networks

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Relating Optimization Problems to Systems of Inequalities and Equalities

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American Journal of Operations Research 2020年第6期10卷 284-298页

作者： H. W. Corley E. O. Dwobeng center on stochastic modeling Optimization and Statistics (COSMOS) The University of Texas at Arlington Arlington TX USA

In quantitative decision analysis, an analyst applies mathematical models to make decisions. Frequently these models involve an optimization problem to determine the values of the decision variables, a system S of possibly non- linear inequalities and equalities to restrict these variables, or both. In this note, we relate a general nonlinear programming problem to such a system S in such a way as to provide a solution of either by solving the other—with certain limitations. We first start with S and generalize phase 1 of the two-phase simplex method to either solve S or establish that a solution does not exist. A conclusion is reached by trying to solve S by minimizing a sum of artificial variables subject to the system S as constraints. Using examples, we illustrate how this approach can give the core of a cooperative game and an equilibrium for a noncooperative game, as well as solve both linear and nonlinear goal programming problems. Similarly, we start with a general nonlinear p

关键词： Optimization Inequalities and Equalities Goal Programming Games Diophantine Equations

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Resource Allocation for Channel Estimation in Reconfigurable Intelligent Surface-Aided Multi-Cell Networks

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Journal of Communications and Information Networks 2024年第1期9卷 64-79页

作者： Yining Xu Sheng Zhou Department of Electronic Engineering Beijing National Research Center for Information Science and TechnologyTsinghua UniversityBeijing 100084China

Reconfigurable intelligent surface(RIS)is a promising solution to deal with the blockage-sensitivity of millimeter wave band and reduce the high energy consumption caused by network densification. However, deploying large scale RISs may not bring expected performance gain due to significant channel estimation overhead and non-negligible reflected *** this paper,we derive the analytical expressions of the coverage probability, area spectrum efficiency(ASE)and energy efficiency (EE)of a downlink RIS-aided multi-cell *** order to optimize the network performance, we investigate the conditions for the optimal number of training symbols of each antenna-to-antenna and antenna-to-element path (referred to as the optimal unit training overhead) in channel *** study shows that:1)RIS deployment is not“the more, the better”, only when blockage objects are dense should one deploy more RISs;2) the coverage probability is maximized when the unit training overhead is designed as large as possible;3)however,the ASE-and-EE-optimal unit training overhead exists. It is a monotonically increasing function of the frame length and a monotonically decreasing function of the average signal-to-noise-ratio (in the high signal-to-noise-ratio region). Additionally,the optimal unit training overhead is smaller when communication nodes deploy particularly few or many antennas.

关键词： reconfigurable intelligent surface multi-cell network directional transmissions channel estimation resource allocation stochastic geometry

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On the Application of Mixed Models of Probability and Convex Set for Time-Variant Reliability Analysis

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Computer modeling in Engineering & Sciences 2024年第5期139卷 1981-1999页

作者： Fangyi Li Dachang Zhu Huimin Shi center for Research on Leading Technology of Special Equipment School of Mechanical and Electric EngineeringGuangzhou UniversityGuangzhou510006China

In time-variant reliability problems,there are a lot of uncertain variables from different ***,it is important to consider these uncertainties in *** addition,time-variant reliability problems typically involve a complexmultilevel nested optimization problem,which can result in an enormous amount of *** this end,this paper studies the time-variant reliability evaluation of structures with stochastic and bounded uncertainties using a mixed probability and convex set *** this method,the stochastic process of a limit-state function with mixed uncertain parameters is first discretized and then converted into a timeindependent reliability ***,to solve the double nested optimization problem in hybrid reliability calculation,an efficient iterative scheme is designed in standard uncertainty space to determine the most probable point(MPP).The limit state function is linearized at these points,and an innovative random variable is defined to solve the equivalent static reliability analysis *** effectiveness of the proposed method is verified by two benchmark numerical examples and a practical engineering problem.

关键词： Mixed uncertainty probability model convex model time-variant reliability analysis

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Posterior Constraint Selection for Nonnegative Linear Programming

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American Journal of Operations Research 2017年第1期7卷 26-40页

作者： H. W. Corley Alireza Noroziroshan Jay M. Rosenberger center on stochastic modeling Optimization & Statistics (COSMOS) The University of Texas at Arlington Arlington TX USA

Posterior constraint optimal selection techniques (COSTs) are developed for nonnegative linear programming problems (NNLPs), and a geometric interpretation is provided. The posterior approach is used in both a dynamic and non-dynamic active-set framework. The computational performance of these methods is compared with the CPLEX standard linear programming algorithms, with two most-violated constraint approaches, and with previously developed COST algorithms for large-scale problems.

关键词： Linear Programming Nonnegative Linear Programming Large-Scale Problems Active Set Methods Constraint Selection Posterior Method COSTs

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FL-EASGD:Federated Learning Privacy Security Method Based on Homomorphic Encryption

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Computers, Materials & Continua 2024年第5期79卷 2361-2373页

作者： Hao Sun Xiubo Chen Kaiguo Yuan Information Security center State Key Laboratory ofNetworking and Switching TechnologyBeijing University of Posts and TelecommunicationsBeijing100876China

Federated learning ensures data privacy and security by sharing models among multiple computing nodes instead of plaintext ***,there is still a potential risk of privacy leakage,for example,attackers can obtain the original data through model inference ***,safeguarding the privacy of model parameters becomes *** proposed solution involves incorporating homomorphic encryption algorithms into the federated learning ***,the existing federated learning privacy protection scheme based on homomorphic encryption will greatly reduce the efficiency and robustness when there are performance differences between parties or abnormal *** solve the above problems,this paper proposes a privacy protection scheme named Federated Learning-Elastic Averaging stochastic Gradient Descent(FL-EASGD)based on a fully homomorphic encryption ***,this paper introduces the homomorphic encryption algorithm into the FL-EASGD scheme to preventmodel plaintext leakage and realize privacy security in the process ofmodel ***,this paper designs a robust model aggregation algorithm by adding time variables and constraint coefficients,which ensures the accuracy of model prediction while solving performance differences such as computation speed and node anomalies such as downtime of each *** addition,the scheme in this paper preserves the independent exploration of the local model by the nodes of each party,making the model more applicable to the local data ***,experimental analysis shows that when there are abnormalities in the participants,the efficiency and accuracy of the whole protocol are not significantly affected.

关键词： Federated learning homomorphic encryption privacy security stochastic gradient descent

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Using MsfNet to Predict the ISUP Grade of Renal Clear Cell Carcinoma in Digital Pathology Images

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Computers, Materials & Continua 2024年第1期78卷 393-410页

作者： Kun Yang Shilong Chang Yucheng Wang Minghui Wang Jiahui Yang Shuang Liu Kun Liu Linyan Xue College of Quality and Technical Supervision Hebei UniversityBaoding071002China National and Local Joint Engineering Research center of Metrology Instrument and System Hebei UniversityBaoding071002China Hebei Technology Innovation center for Lightweight of New Energy Vehicle Power System Hebei UniversityBaoding071002China

Clear cell renal cell carcinoma(ccRCC)represents the most frequent form of renal cell carcinoma(RCC),and accurate International Society of Urological Pathology(ISUP)grading is crucial for prognosis and treatment *** study presents a new deep network called Multi-scale Fusion Network(MsfNet),which aims to enhance the automatic ISUP grade of ccRCC with digital histopathology pathology *** MsfNet overcomes the limitations of traditional ResNet50 by multi-scale information fusion and dynamic allocation of channel *** model was trained and tested using 90 Hematoxylin and Eosin(H&E)stained whole slide images(WSIs),which were all cropped into 320×320-pixel patches at 40×*** achieved a micro-averaged area under the curve(AUC)of 0.9807,a macro-averaged AUC of 0.9778 on the test *** Gradient-weighted Class Activation Mapping(Grad-CAM)visually demonstrated MsfNet’s ability to distinguish and highlight abnormal areas more effectively than *** t-Distributed stochastic Neighbor Embedding(t-SNE)plot indicates our model can efficiently extract critical features from images,reducing the impact of noise and redundant *** results suggest that MsfNet offers an accurate ISUP grade of ccRCC in digital images,emphasizing the potential of AI-assisted histopathological systems in clinical practice.

关键词： Renal cell carcinoma computer-aided diagnosis pathology image deep learning machine learning

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