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Push-Pull Finite-Time Convergence Distributed Optimization Algorithm 推拉有限时间收敛分布式优化算法
美国计算数学期刊(英文) Pub Date : 2020-01-07 DOI: 10.4236/ajcm.2020.101008
Xiaobiao Chen, Kaixin Yan, Yunhua Gao, Xuefeng Xu, Kang Yan, Jing Wang
{"title":"Push-Pull Finite-Time Convergence Distributed Optimization Algorithm","authors":"Xiaobiao Chen, Kaixin Yan, Yunhua Gao, Xuefeng Xu, Kang Yan, Jing Wang","doi":"10.4236/ajcm.2020.101008","DOIUrl":"https://doi.org/10.4236/ajcm.2020.101008","url":null,"abstract":"With the widespread application of distributed systems, many problems need to be solved urgently. How to design distributed optimization strategies has become a research hotspot. This article focuses on the solution rate of the distributed convex optimization algorithm. Each agent in the network has its own convex cost function. We consider a gradient-based distributed method and use a push-pull gradient algorithm to minimize the total cost function. Inspired by the current multi-agent consensus cooperation protocol for distributed convex optimization algorithm, a distributed convex optimization algorithm with finite time convergence is proposed and studied. In the end, based on a fixed undirected distributed network topology, a fast convergent distributed cooperative learning method based on a linear parameterized neural network is proposed, which is different from the existing distributed convex optimization algorithms that can achieve exponential convergence. The algorithm can achieve finite-time convergence. The convergence of the algorithm can be guaranteed by the Lyapunov method. The corresponding simulation examples also show the effectiveness of the algorithm intuitively. Compared with other algorithms, this algorithm is competitive.","PeriodicalId":64456,"journal":{"name":"美国计算数学期刊(英文)","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43819715","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Computing the Full Non-Rigid Group of Trimethylborane and Cyclohaxane Using Wreath Product 用环积计算三甲基硼烷和环己烷的全非刚性基团
美国计算数学期刊(英文) Pub Date : 2020-01-07 DOI: 10.4236/ajcm.2020.101002
E. Suleiman, M. S. Audu
{"title":"Computing the Full Non-Rigid Group of Trimethylborane and Cyclohaxane Using Wreath Product","authors":"E. Suleiman, M. S. Audu","doi":"10.4236/ajcm.2020.101002","DOIUrl":"https://doi.org/10.4236/ajcm.2020.101002","url":null,"abstract":"This paper computes the group and character table of Trimethylborane and Cyclohaxane. Results show that the groups are isomorphic to the wreath products C3wrC2 and C2wrC6 with orders 81 and 384 and with 17 and 28 conjugacy classes respectively, where Cn denotes a cyclic group of order n.","PeriodicalId":64456,"journal":{"name":"美国计算数学期刊(英文)","volume":"10 1","pages":"23-30"},"PeriodicalIF":0.0,"publicationDate":"2020-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46792962","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Stability Analysis of Chain, Mild and Passive Smoking Model 连锁、轻度和被动吸烟模型的稳定性分析
美国计算数学期刊(英文) Pub Date : 2020-01-07 DOI: 10.4236/ajcm.2020.101003
A. Alshareef, H. Batarfi
{"title":"Stability Analysis of Chain, Mild and Passive Smoking Model","authors":"A. Alshareef, H. Batarfi","doi":"10.4236/ajcm.2020.101003","DOIUrl":"https://doi.org/10.4236/ajcm.2020.101003","url":null,"abstract":"In this paper, the global stability of free smoking equilibrium point was evaluated and presented graphically. The linear stability of a developed mathematical model illustrates the effect on the population of chain, mild and passive smokers. MATLAB programming was used to simulate the solutions, the reproduction number R0 and the nature of the equilibria.","PeriodicalId":64456,"journal":{"name":"美国计算数学期刊(英文)","volume":"10 1","pages":"31-42"},"PeriodicalIF":0.0,"publicationDate":"2020-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41646579","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 9
Synchronized Cycles of Generalized Nicholson-Bailey Model 广义Nicholson-Bailey模型的同步环
美国计算数学期刊(英文) Pub Date : 2020-01-07 DOI: 10.4236/ajcm.2020.101009
T. Azizi, G. Kerr
{"title":"Synchronized Cycles of Generalized Nicholson-Bailey Model","authors":"T. Azizi, G. Kerr","doi":"10.4236/ajcm.2020.101009","DOIUrl":"https://doi.org/10.4236/ajcm.2020.101009","url":null,"abstract":"In this paper, we study a drive-response discrete-time dynamical system which has been coupled using convex functions and we introduce a synchronization threshold which is crucial for the synchronizing procedure. We provide one application of this type of coupling in synchronized cycles of a generalized Nicholson-Bailey model. This model demonstrates a rich cascade of complex dynamics from stable fixed point to periodic orbits, quasi periodic orbits and chaos. We explain how this way of coupling makes these two chaotic systems starting from very different initial conditions, quickly get synchronized. We investigate the qualitative behavior of GNB model and its synchronized model using time series analysis and its long time dynamics by the help of bifurcation diagram.","PeriodicalId":64456,"journal":{"name":"美国计算数学期刊(英文)","volume":"10 1","pages":"147-166"},"PeriodicalIF":0.0,"publicationDate":"2020-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48286728","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Constructive Theory of Designing Optimal Eighth-Order Derivative-Free Methods for Solving Nonlinear Equations 求解非线性方程的最优八阶无导数方法的构造理论
美国计算数学期刊(英文) Pub Date : 2020-01-07 DOI: 10.4236/ajcm.2020.101007
T. Zhanlav, Kh. Otgondorj, Renchin-Ochir Mijiddorj
{"title":"Constructive Theory of Designing Optimal Eighth-Order Derivative-Free Methods for Solving Nonlinear Equations","authors":"T. Zhanlav, Kh. Otgondorj, Renchin-Ochir Mijiddorj","doi":"10.4236/ajcm.2020.101007","DOIUrl":"https://doi.org/10.4236/ajcm.2020.101007","url":null,"abstract":"This paper stresses the theoretical nature of constructing the optimal derivative-free iterations. We give necessary and sufficient conditions for derivative-free three-point iterations with the eighth-order of convergence. We also establish the connection of derivative-free and derivative presence three-point iterations. The use of the sufficient convergence conditions allows us to design wide class of optimal derivative-free iterations. The proposed family of iterations includes not only existing methods but also new methods with a higher order of convergence.","PeriodicalId":64456,"journal":{"name":"美国计算数学期刊(英文)","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44839118","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Application of Equality Test of Coefficients of Variation to the Heteroskedasticity Test 变差系数相等检验在异方差检验中的应用
美国计算数学期刊(英文) Pub Date : 2020-01-07 DOI: 10.4236/ajcm.2020.101005
Josoa Michel Tovohery, André Totohasina, Feno Daniel Rajaonasy
{"title":"Application of Equality Test of Coefficients of Variation to the Heteroskedasticity Test","authors":"Josoa Michel Tovohery, André Totohasina, Feno Daniel Rajaonasy","doi":"10.4236/ajcm.2020.101005","DOIUrl":"https://doi.org/10.4236/ajcm.2020.101005","url":null,"abstract":"The presence of heteroskedasticity in a considered regression model may bias the standard deviations of parameters obtained by the Ordinary Least Square (OLS) method. In this case, several hypothesis tests on the model under consideration may be biased, for example, CHOW’s coefficient stability test (or structural change test), Student’s t-test and Fisher’s F-test. Most of the heteroscedasticity tests in the literature are based on the comparison of variances. Despite the multiplication of equality tests of coefficients of variation (CVs) that have appeared in the literature, to our knowledge, the first and only use of the coefficient of variation in the detection of heteroskedasticity was offered by Li and Yao in 2017. Thus, this paper offers an approach to determine the existence of heteroskedasticity by a test of equality of coefficients of variation. We verify by a Monte Carlo robustness and performance test that our method seems even better than some tests in the literature. The results of this study contribute to the exploitation of the statistical measurement of CV dispersion. They help technicians economists to better verify their hypotheses before making a scientific decision when making a necessary forecast, in order to contribute effectively to the economic and sustainable development of a company or enterprise.","PeriodicalId":64456,"journal":{"name":"美国计算数学期刊(英文)","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48649127","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
A Scaled Conjugate Gradient Method Based on New BFGS Secant Equation with Modified Nonmonotone Line Search 基于改进非单调线搜索的新BFGS割线方程的标度共轭梯度法
美国计算数学期刊(英文) Pub Date : 2020-01-07 DOI: 10.4236/ajcm.2020.101001
Tsegay Giday Woldu, Haibin Zhang, Yemane Hailu Fissuh
{"title":"A Scaled Conjugate Gradient Method Based on New BFGS Secant Equation with Modified Nonmonotone Line Search","authors":"Tsegay Giday Woldu, Haibin Zhang, Yemane Hailu Fissuh","doi":"10.4236/ajcm.2020.101001","DOIUrl":"https://doi.org/10.4236/ajcm.2020.101001","url":null,"abstract":"In this paper, we provide and analyze a new scaled conjugate gradient method and its performance, based on the modified secant equation of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method and on a new modified nonmonotone line search technique. The method incorporates the modified BFGS secant equation in an effort to include the second order information of the objective function. The new secant equation has both gradient and function value information, and its update formula inherits the positive definiteness of Hessian approximation for general convex function. In order to improve the likelihood of finding a global optimal solution, we introduce a new modified nonmonotone line search technique. It is shown that, for nonsmooth convex problems, the proposed algorithm is globally convergent. Numerical results show that this new scaled conjugate gradient algorithm is promising and efficient for solving not only convex but also some large scale nonsmooth nonconvex problems in the sense of the Dolan-More performance profiles.","PeriodicalId":64456,"journal":{"name":"美国计算数学期刊(英文)","volume":"10 1","pages":"1-22"},"PeriodicalIF":0.0,"publicationDate":"2020-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46158460","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Illustrative Application of the 2nd-Order Adjoint Sensitivity Analysis Methodology to a Paradigm Linear Evolution/Transmission Model: Reaction-Rate Detector Response 二阶伴随灵敏度分析方法在范例线性演化/传输模型中的应用:反应速率检测器响应
美国计算数学期刊(英文) Pub Date : 2020-01-01 DOI: 10.4236/ajcm.2020.103020
D. Cacuci
{"title":"Illustrative Application of the 2nd-Order Adjoint Sensitivity Analysis Methodology to a Paradigm Linear Evolution/Transmission Model: Reaction-Rate Detector Response","authors":"D. Cacuci","doi":"10.4236/ajcm.2020.103020","DOIUrl":"https://doi.org/10.4236/ajcm.2020.103020","url":null,"abstract":"This work continues the illustrative application of the “Second Order Comprehensive Adjoint Sensitivity Analysis Methodology” (2nd-CASAM) to a benchmark mathematical model that can simulate the evolution and/or transmission of particles in a heterogeneous medium. The model response considered in this work is a reaction-rate detector response, which provides the average interactions of particles with the respective detector or, alternatively, the time-average of the concentration of a mixture of substances in a medium. The definition of this model response includes both uncertain boundary points of the benchmark, thereby providing both direct and indirect contributions to the response sensitivities stemming from the boundaries. The exact expressions for the 1stand 2nd-order response sensitivities to the boundary and model parameters obtained in this work can serve as stringent benchmarks for inter-comparing the performances of all (deterministic and statistical) sensitivity analysis methods.","PeriodicalId":64456,"journal":{"name":"美国计算数学期刊(英文)","volume":"6 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70509260","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
A Sufficient Convexity Condition for Parametric Bézier Surface over Rectangle 矩形上参数曲面的一个充分凸性条件
美国计算数学期刊(英文) Pub Date : 2020-01-01 DOI: 10.4236/ajcm.2020.102013
Sai Hao, Xianghuai Dong
{"title":"A Sufficient Convexity Condition for Parametric Bézier Surface over Rectangle","authors":"Sai Hao, Xianghuai Dong","doi":"10.4236/ajcm.2020.102013","DOIUrl":"https://doi.org/10.4236/ajcm.2020.102013","url":null,"abstract":"Surface convexity is a key issue in computer aided geometric design, which is widely applied in geometric modeling field, such as physical models, industrial design, automatic manufacturing, etc. In this paper, a sufficient convexity condition of the parametric Bezier surface over rectangles is proposed, which is firstly considered as a sufficient convexity condition for the Bezier control grid. The condition is proved by De Casteljau surface subdivision arithmetic, in which the recursive expressions elaborate that the control grid eventually converges to the surface. At last, two examples for the modeling of interpolation-type surface are discussed, one of which is a general surface and the other is a degenerate surface.","PeriodicalId":64456,"journal":{"name":"美国计算数学期刊(英文)","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70509246","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Review on the Current Stochastic Numerical Methods for Econometric Analysis 当前计量经济学分析的随机数值方法综述
美国计算数学期刊(英文) Pub Date : 2019-12-26 DOI: 10.4236/AJCM.2019.94024
Lewis N. K. Mambo, R. M. Mabela, Jean-Pièrre B. Bosonga, Eugène M. Mbuyi
{"title":"Review on the Current Stochastic Numerical Methods for Econometric Analysis","authors":"Lewis N. K. Mambo, R. M. Mabela, Jean-Pièrre B. Bosonga, Eugène M. Mbuyi","doi":"10.4236/AJCM.2019.94024","DOIUrl":"https://doi.org/10.4236/AJCM.2019.94024","url":null,"abstract":"The main aim of this paper is to present and emphasize the contribution of stochastic numerical methods as must tools for the modern econometric modelisation. Indeed, the stochastic numerical methods play an important role in mathematical modelling and the econometric analysis because they model uncertainties that govern the real-world data. However these powerful tools are not well-known and understood by many economists and financial econometricians.","PeriodicalId":64456,"journal":{"name":"美国计算数学期刊(英文)","volume":"9 1","pages":"328-347"},"PeriodicalIF":0.0,"publicationDate":"2019-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46471997","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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