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From mean field games to Navier-Stokes equations 从野外游戏到纳维-斯托克斯方程
IF 1.3
Numerical Algebra Control and Optimization Pub Date : 2021-07-06 DOI: 10.3934/naco.2022020
T. Luo, Q. Song
{"title":"From mean field games to Navier-Stokes equations","authors":"T. Luo, Q. Song","doi":"10.3934/naco.2022020","DOIUrl":"https://doi.org/10.3934/naco.2022020","url":null,"abstract":"<p style='text-indent:20px;'>This work establishes the equivalence between Mean Field Game and a class of PDE systems closely related to compressible Navier-Stokes equations. The solvability of the PDE system via the existence of the Nash Equilibrium of the Mean Field Game is provided under a set of conditions.</p>","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":"98 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2021-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73252981","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
Deep neural nets with fixed bias configuration 具有固定偏置配置的深度神经网络
IF 1.3
Numerical Algebra Control and Optimization Pub Date : 2021-07-03 DOI: 10.3934/naco.2022016
Harbir Antil, Thomas S. Brown, R. Lohner, F. Togashi, Deepanshu Verma
{"title":"Deep neural nets with fixed bias configuration","authors":"Harbir Antil, Thomas S. Brown, R. Lohner, F. Togashi, Deepanshu Verma","doi":"10.3934/naco.2022016","DOIUrl":"https://doi.org/10.3934/naco.2022016","url":null,"abstract":"For any given neural network architecture a permutation of weights and biases results in the same functional network. This implies that optimization algorithms used to 'train' or 'learn' the network are faced with a very large number (in the millions even for small networks) of equivalent optimal solutions in the parameter space. To the best of our knowledge, this observation is absent in the literature. In order to narrow down the parameter search space, a novel technique is introduced in order to fix the bias vector configurations to be monotonically increasing. This is achieved by augmenting a typical learning problem with inequality constraints on the bias vectors in each layer. A Moreau-Yosida regularization based algorithm is proposed to handle these inequality constraints and a theoretical convergence of this algorithm is established. Applications of the proposed approach to standard trigonometric functions and more challenging stiff ordinary differential equations arising in chemically reacting flows clearly illustrate the benefits of the proposed approach. Further application of the approach on the MNIST dataset within TensorFlow, illustrate that the presented approach can be incorporated in any of the existing machine learning libraries.","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":"33 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2021-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82930534","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: 4
Nonlinear Algebra and Applications 非线性代数及其应用
IF 1.3
Numerical Algebra Control and Optimization Pub Date : 2021-03-30 DOI: 10.3934/naco.2021045
Paul Breiding, Turku Ozlum cCelik, Timothy Duff, Alexander Heaton, Aida Maraj, Anna-Laura Sattelberger, Lorenzo Venturello, Ouguzhan Yuruk
{"title":"Nonlinear Algebra and Applications","authors":"Paul Breiding, Turku Ozlum cCelik, Timothy Duff, Alexander Heaton, Aida Maraj, Anna-Laura Sattelberger, Lorenzo Venturello, Ouguzhan Yuruk","doi":"10.3934/naco.2021045","DOIUrl":"https://doi.org/10.3934/naco.2021045","url":null,"abstract":"We showcase applications of nonlinear algebra in the sciences and engineering. Our review is organized into eight themes: polynomial optimization, partial differential equations, algebraic statistics, integrable systems, configuration spaces of frameworks, biochemical reaction networks, algebraic vision, and tensor decompositions. Conversely, developments on these topics inspire new questions and algorithms for algebraic geometry.","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":"63 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2021-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86505214","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: 8
Inertial method for split null point problems with pseudomonotone variational inequality problems 带伪单调变分不等式的分裂零点问题的惯性方法
IF 1.3
Numerical Algebra Control and Optimization Pub Date : 2021-01-01 DOI: 10.3934/naco.2021037
C. C. Okeke, A. Bello, L. Jolaoso, Kingsley Chimuanya Ukandu
{"title":"Inertial method for split null point problems with pseudomonotone variational inequality problems","authors":"C. C. Okeke, A. Bello, L. Jolaoso, Kingsley Chimuanya Ukandu","doi":"10.3934/naco.2021037","DOIUrl":"https://doi.org/10.3934/naco.2021037","url":null,"abstract":"This paper analyzed the new extragradient type algorithm with inertial extrapolation step for solving self adaptive split null point problem and pseudomonotone variational inequality in real Hilbert space. Furthermore, in this study, a strong convergence result is obtained without assuming Lipschitz continuity of the associated mapping and the operator norm is self adaptive. Additionally, the proposed algorithm only uses one projections onto the feasible set in each iteration. More so, the strong convergence results are obtained under some relaxed conditions on the initial factor and the iterative parameters. Numerical results are presented to illustrate the performance of the proposed algorithm.The results obtained in this study improved and extended related studies in the literature.","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":"243 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89054861","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: 4
Some representations of moore-penrose inverse for the sum of two operators and the extension of the fill-fishkind formula 两个算子和的moore-penrose逆的一些表示及填充-鱼类公式的推广
IF 1.3
Numerical Algebra Control and Optimization Pub Date : 2021-01-01 DOI: 10.3934/NACO.2021015
Abdessalam Kara, S. Guedjiba
{"title":"Some representations of moore-penrose inverse for the sum of two operators and the extension of the fill-fishkind formula","authors":"Abdessalam Kara, S. Guedjiba","doi":"10.3934/NACO.2021015","DOIUrl":"https://doi.org/10.3934/NACO.2021015","url":null,"abstract":"In the setting of arbitrary Hilbert spaces, we give a representation of M-P inverse of the sum of linear operators begin{document}$ A+B $end{document} under suitable conditions. Based on the full-rank decomposition of an operator, we prove that the extension of the Fill-Fishkind formula for begin{document}$ A $end{document} and begin{document}$ B $end{document} with closed ranges, remains valid, keeping the same conditions of Fill-Fishkind formula for two matrices, also we obtain an analogous formula under the Fill-Fishkind conditions, beyond we derive some representations of M-P inverse of a 2-by-2 block operator with disjoint ranges.","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":"225 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73619920","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Convergence of interval AOR method for linear interval equations 线性区间方程的区间AOR方法的收敛性
IF 1.3
Numerical Algebra Control and Optimization Pub Date : 2021-01-01 DOI: 10.3934/NACO.2021006
Jahnabi Chakravarty, Ashiho Athikho, M. Saha
{"title":"Convergence of interval AOR method for linear interval equations","authors":"Jahnabi Chakravarty, Ashiho Athikho, M. Saha","doi":"10.3934/NACO.2021006","DOIUrl":"https://doi.org/10.3934/NACO.2021006","url":null,"abstract":"A real interval vector/matrix is an array whose entries are real intervals. In this paper, we consider the real linear interval equations begin{document}$ bf{Ax} = bf{b} $end{document} with begin{document}$ {{bf{A}} }$end{document} , begin{document}$ bf{b} $end{document} respectively, denote an interval matrix and an interval vector. The aim of the paper is to study the numerical solution of the linear interval equations for various classes of coefficient interval matrices. In particular, we study the convergence of interval AOR method when the coefficient interval matrix is either interval strictly diagonally dominant matrices, interval begin{document}$ L $end{document} -matrices, interval begin{document}$ M $end{document} -matrices, or interval begin{document}$ H $end{document} -matrices.","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":"91 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78594051","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
A PID control method based on optimal control strategy 基于最优控制策略的PID控制方法
IF 1.3
Numerical Algebra Control and Optimization Pub Date : 2021-01-01 DOI: 10.3934/naco.2020019
H. Niu, Zhi Feng, Qijin Xiao, Yajun Zhang
{"title":"A PID control method based on optimal control strategy","authors":"H. Niu, Zhi Feng, Qijin Xiao, Yajun Zhang","doi":"10.3934/naco.2020019","DOIUrl":"https://doi.org/10.3934/naco.2020019","url":null,"abstract":"A PID control method which combined optimal control strategy is proposed in this paper. The posterior unmodeled dynamics measurement data information are made full use to compensate the unknown nonlinearity of the system, and the unknown increment of the unmodeled dynamics is estimated. Then, a nonlinear PID controller with compensation of the posterior unmodeled dynamics measurement data and the estimation of the increment of the unmodeled dynamics is designed. Finally, through the numerical simulation, the effectiveness of the proposed method is vertified.","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":"33 1 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78647569","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
Modified inertial algorithm for solving mixed equilibrium problems in Hadamard spaces 求解Hadamard空间混合平衡问题的改进惯性算法
IF 1.3
Numerical Algebra Control and Optimization Pub Date : 2021-01-01 DOI: 10.3934/naco.2021039
A. Khan, C. Izuchukwu, M. Aphane, G. C. Ugwunnadi
{"title":"Modified inertial algorithm for solving mixed equilibrium problems in Hadamard spaces","authors":"A. Khan, C. Izuchukwu, M. Aphane, G. C. Ugwunnadi","doi":"10.3934/naco.2021039","DOIUrl":"https://doi.org/10.3934/naco.2021039","url":null,"abstract":"The main purpose of this paper is to introduce the concept of modified inertial algorithm in Hadamard spaces. We emphasize that, as far as we know, this is the first time that this concept is being considered in this setting. Under some weak assumptions, we prove that the modified inertial algorithm converges strongly to a common solution of a finite family of mixed equilibrium problems and fixed point problem of a nonexpansive mapping. We also give a primary numerical illustration in the framework of Hadamard spaces, to show the efficiency of the modified inertial term in our proposed algorithm.","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":"16 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87331855","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
Time-optimal of fixed wing UAV aircraft with input and output constraints 具有输入和输出约束的固定翼无人机时间优化
IF 1.3
Numerical Algebra Control and Optimization Pub Date : 2021-01-01 DOI: 10.3934/naco.2021023
M. H. Shavakh, B. Bidabad
{"title":"Time-optimal of fixed wing UAV aircraft with input and output constraints","authors":"M. H. Shavakh, B. Bidabad","doi":"10.3934/naco.2021023","DOIUrl":"https://doi.org/10.3934/naco.2021023","url":null,"abstract":"The route prediction of unmanned aerial vehicles (UAVs) according to their missions is a strategic issue in the aviation field. In some particular missions, the UAV tasks are to start a movement from a defined point to a target reign in the shortest time. This paper proposes a practical method to find the guidance law of the fixed-wing UAV to achieve time-optimal considering the ambient wind. The unique features of this paper are that the environment includes the moving and fixed obstacles as the route constraints, and the fixed-wing UAVs have to keep a given distance from these obstacles. Also, we consider the specific kinematic equation of the fixed-wing UAV and limitations on the flight-path angle and bank-angles as other constraints. We suggest a method for controlling a fixed-wing UAV to get time-optimal using the re-scaling and parameterization techniques. These techniques are useful and effective in maximizing the performance of the gradient-based methods as a sequential quadratic programming method ( begin{document}$ SQP $end{document} ) for numerical solutions. Then, all constraints of the time-optimal control problem are converted to a constraint using an exact penalty function. Due to being exact, finding the control variables and switching times is more accurate and faster. Finally, some numerical examples are simulated to explore the effectiveness of our proposed study in reality.","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":"25 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80603479","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: 1
General biconvex functions and bivariational inequalities 一般双凸函数与二分不等式
IF 1.3
Numerical Algebra Control and Optimization Pub Date : 2021-01-01 DOI: 10.3934/naco.2021041
M. Noor, K. Noor
{"title":"General biconvex functions and bivariational inequalities","authors":"M. Noor, K. Noor","doi":"10.3934/naco.2021041","DOIUrl":"https://doi.org/10.3934/naco.2021041","url":null,"abstract":"In this paper, we define and introduce some new concepts of the higher order strongly general biconvex functions involving the arbitrary bifunction and a function. Some new relationships among various concepts of higher order strongly general biconvex functions have been established. It is shown that the new parallelogram laws for Banach spaces can be obtained as applications of higher order strongly affine general biconvex functions, which is itself an novel application. It is proved that the optimality conditions of the higher order strongly general biconvex functions are characterized by a class of variational inequalities, which is called the higher order strongly general bivariational inequality. Auxiliary principle technique is used to suggest an implicit method for solving strongly general bivariational inequalities. Convergence analysis of the proposed method is investigated using the pseudo-monotonicity of the operator. Some special cases also discussed. Results obtained in this paper can be viewed as refinement and improvement of previously known results.","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":"56 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81018746","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
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