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SEMI-PROXIMAL POINT METHOD FOR NONSMOOTH CONVEX-CONCAVE MINIMAX OPTIMIZATION

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Journal of Computational Mathematics 2024年第3期42卷 617-637页

作者： Yuhong Dai Jiani Wang Liwei Zhang LSEC ICMSECAMSSChinese Academy of SciencesBeijing 100190China School of Mathematical SciencesUniversity of Chinese Academy of SciencesBeijing 100049China Academy of Mathematics and Systems Science Chinese Academy of SciencesBeijing 100190China school of mathematical sciences Dalian University of TechnologyDalian 116024China

Minimax optimization problems are an important class of optimization problems arising from modern machine learning and traditional research *** there have been many numerical algorithms for solving smooth convex-concave minimax problems,numerical algorithms for nonsmooth convex-concave minimax problems are *** paper aims to develop an efficient numerical algorithm for a structured nonsmooth convex-concave minimax problem.A semi-proximal point method(SPP)is proposed,in which a quadratic convex-concave function is adopted for approximating the smooth part of the objective function and semi-proximal terms are added in each *** construction enables the subproblems at each iteration are solvable and even easily solved when the semiproximal terms are cleverly *** prove the global convergence of our algorithm under mild assumptions,without requiring strong convexity-concavity *** the locally metrical subregularity of the solution mapping,we prove that our algorithm has the linear rate of *** numerical results are reported to verify the efficiency of our algorithm.

关键词： Minimax optimization Convexity-concavity Global convergence Rate of con-vergence Locally metrical subregularity

Stochastic Maximum Principle for Square-Integrable Optimal Control of Linear Stochastic Systems

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Chinese Annals of Mathematics,Series B 2024年第5期45卷 661-676页

作者： Shanjian TANG Xueqi WANG Department of Finance and Control sciences School of Mathematical Sciences Fudan University school of mathematical sciences Fudan University

The authors give a stochastic maximum principle for square-integrable optimal control of linear stochastic systems. The control domain is not necessarily convex and the cost functional can have a quadratic growth. In ... 详细信息

关键词： 60H10 93E20 Linear stochastic system Optimal control Square integrability Stochastic maximum principle

NORMALIZED SOLUTIONS FOR THE GENERAL KIRCHHOFF TYPE EQUATIONS

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Acta Mathematica Scientia 2024年第5期44卷 1886-1902页

作者： Wenmin LIU Xuexiu ZHONG Jinfang ZHOU school of mathematical sciences South China Normal UniversityGuangzhou510631China South China Research Center for Applied Mathematics and Interdisciplinary Studies&school of mathematical sciences South China Normal UniversityGuangzhou510631China

In the present paper,we prove the existence,non-existence and multiplicity of positive normalized solutions(λ_(c),u_(c))∈ℝ×H^(1)(ℝ^(N))to the general Kirchhoff problem-M\left(\int_{\mathbb{R}^N}\vert\nabla u\vert^2{\rm d}x\right)\Delta u+\lambda u=g(u)~\hbox{in}~\mathbb{R}^N,u\in H^1(\mathbb{R}^N),N\geq 1,satisfying the normalization constraint\int_{\mathbb{R}^N}u^2{\rm d}x=c,where M∈C([0,∞))is a given function satisfying some suitable *** argument is not by the classical variational method,but by a global branch approach developed by Jeanjean et al.[J Math Pures Appl,2024,183:44–75]and a direct correspondence,so we can handle in a unified way the nonlinearities g(s),which are either mass subcritical,mass critical or mass supercritical.

关键词： normalized solution Kirchhoff type equations general nonlinearities asymptotic behavior

Training Generative Adversarial Networks with Adaptive Composite Gradient

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Data Intelligence 2024年第1期6卷 120-157页

作者： Huiqing Qi Fang Li Shengli Tan Xiangyun Zhang school of mathematical sciences East China Normal UniversityShanghai 200241China

The wide applications of Generative adversarial networks benefit from the successful training methods,guaranteeing that an object function converges to the local ***,designing an efficient and competitive training method is still a challenging task due to the cyclic behaviors of some gradient-based ways and the expensive computational cost of acquiring the Hessian *** address this problem,we proposed the Adaptive Composite Gradients(ACG)method,linearly convergent in bilinear games under suitable *** analysis and toy-function experiments both suggest that our approach alleviates the cyclic behaviors and converges faster than recently proposed SOTA *** convergence speed of the ACG is improved by 33%than other *** ACG method is a novel Semi-Gradient-Free algorithm that can reduce the computational cost of gradient and Hessian by utilizing the predictive information in future *** mixture of Gaussians experiments and real-world digital image generative experiments show that our ACG method outperforms several existing technologies,illustrating the superiority and efficacy of our method.

关键词： Generative adversarial networks adaptive composite gradient semi-gradient free game theory bilinear game

ON QK（p）-TEICHMüLLER SPACES

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Acta Mathematica Scientia 2024年第6期44卷 2283-2295页

作者：漆毅吴艳 school of mathematical sciences Beihang University school of Mathematics and Statistics Linyi University

The QK（p）-Teichmüller space is introduced and studied in this *** characterizations of the QK（p）-Teichmüller space and the QK,0（p）-Teichmüller space are *** Schwarzian derivative model and pre-logarithmic der... 详细信息

关键词： 30C62 30F60 30H25 Carleson measure pre-logarithmic derivative QK(p, q) spaces Schwarzian derivative universal Teichmüller space

Novel Partitioned Time-Stepping Algorithms for Fast Computation of Random Interface-Coupled Problems with Uncertain Parameters

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Numerical Mathematics(Theory,Methods and Applications) 2024年第1期17卷 145-180页

作者： Yizhong Sun Jiangshan Wang Haibiao Zheng school of mathematical sciences East China Normal UniversityShanghaiChina school of mathematical sciences Ministry of Education Key Laboratory of Mathematics and Engineering ApplicationsShanghai Key Laboratory of PMMPEast China Normal UniversityShanghaiChina

The simulation of multi-domain,multi-physics mathematical models with uncertain parameters can be quite demanding in terms of algorithm design and com-putation *** main objective in this paper is to examine a physical interface coupling between two random dissipative systems with uncertain *** to the complexity and uncertainty inherent in such interface-coupled problems,un-certain diffusion coefﬁcients or friction parameters often arise,leading to consid-ering random *** employ Monte Carlo methods to produce independent and identically distributed deterministic heat-heat model samples to address ran-dom systems,and adroitly integrate the ensemble idea to facilitate the fast calcu-lation of these *** achieve unconditional stability,we introduce the scalar auxiliary variable(SAV)method to overcome the time constraints of the ensemble implicit-explicit ***,for a more accurate and stable scheme,the ensemble data-passing algorithm is raised,which is unconditionally stable and convergent without any auxiliary *** algorithms employ the same co-efﬁcient matrix for multiple linear systems and enable easy parallelization,which can signiﬁcantly reduce the computational ***,numerical experiments are conducted to support the theoretical results and showcase the unique features of the proposed algorithms.

关键词： Scalar auxiliary variable,ensemble algorithm,random interface-coupled problems,implicit-explicit partitioned method,data-passing partitioned method

Spin-based magnetic random-access memory for high-performance computing

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National Science Review 2024年第3期11卷 20-23页

作者： Kaiming Cai Tianli Jin Wen Siang Lew school of Physics Huazhong University of Science and Technology Interuniversity Microelectronics Centre(IMEC) school of Physical and mathematical sciences Nanyang Technological University

Memory serves as a critical component in today's electronic systems for data storage and processing. In traditional computer architectures, the logic and memory units are physically separated, due to the performance gap in operational speed and capacity among memories, resulting in the fundamental limitation of the von Neumann computers.

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Fixed-Time Cluster Optimization for Multi-Agent Systems Based on Piecewise Power-Law Design

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IEEE/CAA Journal of Automatica Sinica 2024年第5期11卷 1301-1303页

作者： Suna Duan Xinchun Jia Xiaobo Chi school of mathematical sciences Shanxi UniversityTaiyuan 030006China school of Automation and Software Engineering Shanxi UniversityTaiyuan 030013China

Dear Editor,This letter focuses on the fixed-time(FXT)cluster optimization problem of first-order multi-agent systems(FOMASs)in an undirected network,in which the optimization objective is the sum of the objective functions of all clusters.A novel piecewise power-law control protocol with cooperative-competition relations is ***,a sufficient condition is obtained to ensure that the FOMASs achieve the cluster consensus within an FXT.

关键词： agent cluster optimization

Some Modified Equations of the Sine-Hilbert Type

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Chinese Physics Letters 2024年第4期41卷 1-6页

作者：闫铃娟刘亚杰胡星标 LSEC ICMSECAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China school of mathematical sciences University of Chinese Academy of SciencesBeijing 100049China

Three modified sine-Hilbert(sH)-type equations, i.e., the modified sH equation, the modified damped sH equation, and the modified nonlinear dissipative system, are proposed, and their bilinear forms are *** on these b... 详细信息

关键词： bilinear equations equation