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A Linearly Convergent Douglas-Rachford Splitting Solver for Markovian Information-Theoretic Optimization Problems

IEEE TRANSACTIONS ON INFORMATION THEORY 2023年第5期69卷 3372-3399页

作者： Huang, Teng-Hui El Gamal, Aly El Gamal, Hesham Purdue Univ Dept Elect & Comp Engn W Lafayette IN 47907 USA Univ Sydney Dept Elect & Informat Engn Camperdown NSW 2006 Australia InterDigital Wilmington DE 19809 USA Amazon Com Los Angeles CA 90232 USA

In this work, we propose solving the Information Bottleneck (IB) and Privacy Funnel (PF) problems with Douglas-Rachford Splitting methods (DRS). We study a general Markovian information-theoretic Lagrangian that includes IB and PF into a unified framework. We prove the linear convergence of the proposed solvers using the Kurdyka- ojasiewicz inequality. Moreover, our analysis is beyond IB and PF and applies to any convex-weakly convex pair objectives. Based on the results, we develop two types of linearly convergent IB solvers, with one improves the performance of convergence over existing solvers while the other can be independent to the relevance-compression trade-off. Moreover, our results apply to PF, yielding a new class of linearly convergent PF solvers. Empirically, the proposed IB solvers IB obtain solutions that are comparable to the Blahut-Arimoto-based benchmark and is convergent for a wider range of the penalty coefficients than existing solvers. For PF, our non-greedy solvers can characterize the privacy-utility trade-off better than the clustering-based greedy solvers.

关键词： Convergence Optimization Information theory Privacy Markov processes Mutual information Machine learning information bottleneck (IB) privacy funnel (PF) source coding convergence iterative algorithm optimization methods gradient methods Lagrangian functions

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Coverage Performance Evaluation for Cellular Networks With Correlated Blockage Model

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IEEE COMMUNICATIONS LETTERS 2023年第2期27卷 736-740页

作者： Liu, Bin Song, Rongfang Nanjing Univ Posts & Telecommun Coll Telecommun & Informat Engn Nanjing 210003 Peoples R China

Analyzing correlation effects caused by the realistic geometry of blockage is crucial to evaluate network performance in wireless networks. However, the correlation generally complicates analysis procedure even makes it intractable. Based on the cascade blockage model, this letter proposes a functional framework for performance evaluation from a vision of typical user. We first derive a functional equation to obtain the association probability that can be solved efficiently by an association iterative algorithm. Then, they are leveraged to design a coverage iterative algorithm to analyze the coverage probability in the form of joint distribution. This analytical framework gains insight into the effect of blockage correlation and penetration loss on network performance. In addition, it is applied to inter-cell interference coordination (ICIC) context to demonstrate its feasibility and flexibility.

关键词： Mathematical models iterative methods Geometry Correlation Interference Adaptation models Intercell interference Stochastic geometry cascade blockage model iterative algorithm association probability coverage probability

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A NEW CLASS OF VARIATIONAL-LIKE INCLUSION PROBLEMS: algorithmIC AND ANALYTICAL APPROACH

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JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION 2023年第9期19卷 6364-6397页

作者： Balooee, Javad Chang, Shih-Sen Yao, Jen-Chih Univ Tehran Sch Math Stat & Comp Sci Coll Sci Tehran Iran China Med Univ Ctr Gen Educ Taichung 40402 Taiwan

The main contribution of this work is the construction of a new iterative algorithm with the help of the notion of resolvent operator associated with an (A) over cap -maximal m-relaxed eta-accretive mapping for solving a new class of set-valued variational-like inclusion problems in the setting of Banach spaces. The convergence analysis of the iterative sequences generated by our proposed iterative algorithm is studied under some appropriate conditions. The main attention of the final section is paid to the investigating and analysis of the notion of (H (., .), eta)-accretive operator introduced and studied by Wang and Ding (2010). In the light of the considered conditions for an (H (., .), eta)-accretive operator, we point out that every (H (., .), eta)-accretive operator is actually an (A) over cap -maximal m-relaxed eta-accretive mapping and is not a new one. Finally, our paper is closed with some important comments regarding (H (., .), eta)-accretive operator and the derived results related to it in the literature.

关键词： Set-valued variational-like inclusion problem (A)over-cap-maximal m-relaxed eta-accretive mapping resolvent operator (H(., .), eta)-accretive operator iterative algorithm convergence analysis

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A Novel Halpern-type algorithm for a Monotone Inclusion Problem and a Fixed Points Problem on Hadamard Manifolds

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NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION 2023年第10期44卷 1031-1043页

作者： He, Huimin Peng, Jigen Fan, Qinwei Guangzhou Univ Sch Math & Informat Sci Guangzhou 510006 Peoples R China Xian Polytech Univ Sch Sci Xian Peoples R China

In this paper, we propose a novel Halpern-type algorithm and prove that the sequence generated by the algorithm converges strongly to the common element of the set of fixed points of the two firmly nonexpansive mappings and the solution set of zero points of the monotone inclusion problems on Hadamard manifolds, the main results in this paper extended and improved some recent related results.

关键词： Hadamard manifold fixed points iterative algorithm monotone inclusion problem >

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Feature selection using class-level regularized self-representation

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APPLIED INTELLIGENCE 2023年第11期53卷 13130-13144页

作者： Lu, Zhenghua Chu, Qihuan Univ Chinese Acad Sci Natl Space Sci Ctr Beijing 100190 Peoples R China Harbin Inst Technol Sch Management Harbin 150006 Peoples R China

Feature selection aims at selecting representative features from the original high-dimensional feature set, and it has drawn much attention in most real-world applications like data mining and pattern recognition. This paper studies feature selection problem from the viewpoint of feature self-representation. Traditionally, feature self-representation is only performed on the whole-level reconstruction, whereas the feature selection ability is insufficient owing to the intra-class variations. To address this problem, we propose a new feature selection method, i.e., class-level regularized self-representation (CLRSR). In the proposed method, a class-level reconstruction term is designed to reduce intra-class variations of the samples from different categories. By jointly optimizing the whole-level reconstruction and the class-level reconstruction, CLRSR is able to select more discriminative and informative features. Moreover, an iterative algorithm is proposed to minimize cost function of CLRSR, and its convergence is proven in theory. By comparing with several state-of-the-art feature selection methods, experimental evaluations on six benchmark datasets have verified effectiveness and superiority of CLRSR.

关键词： Feature selection Self-representation Class-level reconstruction iterative algorithm

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On the solutions to Sylvester-conjugate periodic matrix equations via iteration

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IET CONTROL THEORY AND APPLICATIONS 2023年第3期17卷 307-317页

作者： Zhang, Lei Li, Pengxiang Han, Mengqi Zhang, Yanfeng Chang, Rui Zhang, Jinhua Henan Univ Sch Comp & Informat Engn Henan Prov Engn Res Ctr Spatial Informat Proc Henan Key Lab Big Data Anal & Proc Kaifeng 475004 Peoples R China Baoyuan Ind Investment Co Ltd Xinyang Peoples R China North China Univ Water Resources & Elect Power Sch Elect Engn Zhengzhou Peoples R China

The problem of solving a class of Sylvester-conjugate periodic matrix equations is investigated in this paper. Utilising conjugate gradient method, an iterative algorithm is provided, from which a matrix sequence can be generated to approximate the unknown matrix of the equation to be solved. Theoretical derivation proves that the proposed algorithm is convergent starting from any initial value, and simulation examples show the effectiveness of the proposed algorithm.

关键词： iterative algorithm matrix approximation conjugate gradient method Interpolation and function approximation (numerical analysis) Algebra, set theory, and graph theory conjugate gradient methods Numerical approximation and analysis Numerical analysis approximation theory matrix algebra Sylvester-conjugate periodic matrix equations matrix sequence convergence Linear algebra (numerical analysis)

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Maximum Block Energy Guided Robust Subspace Clustering

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IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE 2023年第2期45卷 2652-2659页

作者： Qin, Yalan Zhang, Xinpeng Shen, Liquan Feng, Guorui Shanghai Univ Sch Commun & Informat Engn Shanghai 200444 Peoples R China

Subspace clustering is useful for clustering data points according to the underlying subspaces. Many methods have been presented in recent years, among which Sparse Subspace Clustering (SSC), Low-Rank Representation (LRR) and Least Squares Regression clustering (LSR) are three representative methods. These approaches achieve good results by assuming the structure of errors as a prior and removing errors in the original input space by modeling them in their objective functions. In this paper, we propose a novel method from an energy perspective to eliminate errors in the projected space rather than the input space. Since the block diagonal property can lead to correct clustering, we measure the correctness in terms of a block in the projected space with an energy function. A correct block corresponds to the subset of columns with the maximal energy. The energy of a block is defined based on the unary column, pairwise and high-order similarity of columns for each block. We relax the energy function of a block and approximate it by a constrained homogenous function. Moreover, we propose an efficient iterative algorithm to remove errors in the projected space. Both theoretical analysis and experiments show the superiority of our method over existing solutions to the clustering problem, especially when noise exists.

关键词： Subspace clustering maximum block energy robust constrained homogenous function iterative algorithm

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OPTIMAL CONTROL FOR MULTISCALE ELLIPTIC EQUATIONS WITH ROUGH COEFFICIENTS

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Journal of Computational Mathematics 2023年第5期41卷 841-865页

作者： Yanping Chen Xinliang Liu Jiaoyan Zeng Lei Zhang School of Mathematical Sciences South China Normal UniversityGuangzhou 510631China King Abdullah University of Science and Technology Thuwal 23955Saudi Arabia School of Mathematics and Statistics Guangdong University of FinanceGuangzhou 510631China School of Mathematical Sciences Institute of Natural Sciencesand MOE-LSCShanghai Jiao Tong UniversityShanghai 200240China

This paper concerns the convex optimal control problem governed by multiscale elliptic equations with arbitrarily rough L∞coefficients,which has not only complex coupling between nonseparable scales and nonlinearity,but also important applications in composite materials and *** use one of the recently developed numerical homogenization techniques,the so-called Rough Polyharmonic Splines(RPS)and its generalization(GRPS)for the efficient resolution of the elliptic operator on the coarse *** methods have optimal convergence rate which do not rely on the regularity of the coefficients nor the concepts of scale-separation or *** the iterative solution of the nonlinearly coupled OCP-OPT formulation for the optimal control problem requires solving the corresponding(state and co-state)multiscale elliptic equations many times with different right hand sides,numerical homogenization approach only requires one-time pre-computation on the fine scale and the following iterations can be done with computational cost proportional to coarse degrees of *** experiments are presented to validate the theoretical analysis.

关键词： Optimal control Rough coefficients Multiscale elliptic equations Numerical homogenization Rough polyharmonic splines iterative algorithm

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Differential dynamic programming for finite-horizon zero-sum differential games of nonlinear systems

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INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL 2023年第18期33卷 11062-11084页

作者： Zhang, Bin Jia, Yingmin Zhang, Yuqi Beijing Univ Posts & Telecommun Sch Artificial Intelligence Beijing 100876 Peoples R China Beihang Univ Res Div 7 Beijing Peoples R China

In this article, we present an iterative algorithm based on differential dynamic programming (DDP) for finite-horizon two-person zero-sum differential games. The technique of DDP is used to expand the Hamilton-Jacobi-Isaacs (HJI) partial differential equation into higher-order differential equations. Using value function and saddle point approximations, the DDP expansion is transformed into algebraic matrix equation in integral form. Based on the algebraic matrix equation, a DDP iterative algorithm is developed to learn the solution to the differential games. Strict proof is proposed to guarantee the iterative convergences of the value function and saddle point. The new algorithm is fundamentally different from existing results, in the sense that it overcome the technical obstacle to address the time-varying behavior of HJI partial differential equation. Simulation examples are given to demonstrate the effectiveness of the proposed method.

关键词： differential dynamic programming differential games finite-horizon cost function Hamilton-Jacobi-Isaacs equation iterative algorithm

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Three-dimensional inversion analysis of transient electromagnetic response signals of water-bearing abnormal bodies in tunnels based on numerical characteristic parameters

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MATHEMATICAL BIOSCIENCES AND ENGINEERING 2023年第1期20卷 1106-1121页

作者： Xu, Yikang Sun, Zhaohua Gu, Wei Qian, Wangping Shen, Qiangru Gong, Jian Nantong Univ Sch Transportat & Civil Engn Nantong 226019 Peoples R China Guangxi Univ Guangxi Key Lab Disaster Prevent & Engn Safety Nanning 530004 Peoples R China Rudong Jinheng City Investment Grp Co Ltd Nantong 226400 Peoples R China Guangxi Univ Key Lab Disaster Prevent & Struct Safety Minist Educ Nanning 530004 Peoples R China

The transient electromagnetic inversion of detection signals mainly depends on fast inversion in the half-space state. However, the interpretation results have a certain degree of uncertainty and blindness, so the accuracy and applicability of the three-dimensional full-space inversion need to be investigated. Two different three-dimensional full-space inversions were carried out. First, the numerical characteristic parameters of the response signals were extracted. Then, the correlations between the numerical characteristic parameters and physical parameters of the water -bearing abnormal bodies were judged, and the judgment criterion of the iterative direction was proposed. Finally, the inversion methods of the iterative algorithm and the BP neural network were utilized based on the virtual example samples. The results illustrate that the proposed numerical characteristic parameters can accurately reflect the response curve of the full-space surrounding rock. The difference in the numerical characteristic parameters was used to determine the update direction and correction value. Both inversion methods have their advantages and disadvantages. A single inversion method cannot realize the three-dimensional inversion of the physical parameters of water -bearing abnormal bodies quickly, effectively and intelligently. Therefore, the benefits of different inversion methods need to be considered to comprehensively select a reasonable inversion method. The results can provide essential ideas for the subsequent interpretation of the three-dimensional spatial response signals of water-bearing abnormal bodies.

关键词： water-bearing abnormal bodies transient electromagnetic method response signals three-dimensional inversion iterative algorithm neural network

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