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On greedy randomized coordinate updating iteration methods for solving symmetric eigenvalue problems

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Applied Numerical Mathematics 2025年 216卷 76-97页

作者： Bai, Zhong-Zhi State Key Laboratory of Mathematical Sciences Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China State Key Laboratory of Scientific/Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences P.O. Box 2719 Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China

In order to compute the smallest eigenvalue and its corresponding eigenvector of a large-scale, real, and symmetric matrix, we propose a class of greedy randomized coordinate updating iteration methods based on the principle that the indices of larger entries in absolute value of the current residual are selected with a higher probability and, with respect to this index set, the next iterate is updated from the current iterate along with the selected coordinate such that the corresponding entry of the residual is annihilated, resulting in fast convergence rates of the proposed iteration methods. Under appropriate conditions, we prove the convergence of both sequences of the Rayleigh-quotients and the acute angles between the iterates and the eigenvector in terms of the expectation. By numerical experiments, we show that this class of greedy randomized coordinate updating iteration methods are advantageous over the parameterized power method and the coordinate descent method in both iteration counts and computing times. Moreover, with theoretical analysis and computational performance, we confirm that the convergence property of this class of iteration methods can be improved significantly by suitably choosing the arbitrary nonnegative parameter involved in the greedy probability criterion. © 2025 IMACS

关键词： Eigenvalues and eigenfunctions

A space-decoupling framework for optimization on bounded-rank matrices with orthogonally invariant constraints

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arXiv 2025年

作者： Yang, Yan Gao, Bin Yuan, Ya-Xiang State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences The University of Chinese Academy of Sciences Beijing China State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China

Imposing additional constraints on low-rank optimization has garnered growing interest. However, the geometry of coupled constraints hampers the well-developed low-rank structure and makes the problem intricate. To this end, we propose a space-decoupling framework for optimization on bounded-rank matrices with orthogonally invariant constraints. The "space-decoupling" is reflected in several ways. We show that the tangent cone of coupled constraints is the intersection of tangent cones of each constraint. Moreover, we decouple the intertwined bounded-rank and orthogonally invariant constraints into two spaces, leading to optimization on a smooth manifold. Implementing Riemannian algorithms on this manifold is painless as long as the geometry of additional constraints is known. In addition, we unveil the equivalence between the reformulated problem and the original problem. Numerical experiments on real-world applications—spherical data fitting, graph similarity measuring, low-rank SDP, model reduction of Markov processes, reinforcement learning, and deep learning—validate the superiority of the proposed framework. Copyright © 2025, The Authors. All rights reserved.

关键词： Markov processes

An Adaptive Proximal Inexact Gradient Framework and Its Application to Per-Antenna Constrained Joint Beamforming and Compression Design

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arXiv 2025年

作者： Fan, Xilai Jiang, Bo Liu, Ya-Feng State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China Ministry of Education Key Laboratory of NSLSCS School of Mathematical Sciences Nanjing Normal University Nanjing210023 China

In this paper, we propose an adaptive proximal inexact gradient (APIG) framework for solving a class of nonsmooth composite optimization problems involving function and gradient errors. Unlike existing inexact proximal gradient methods, the proposed framework introduces a new line search condition that jointly adapts to function and gradient errors, enabling adaptive stepsize selection while maintaining theoretical guarantees. Specifically, we prove that the proposed framework achieves an ϵ-stationary point within O(ϵ−2) iterations for nonconvex objectives and an ϵ-optimal solution within O(ϵ−1) iterations for convex cases, matching the best-known complexity in this context. We then custom-apply the APIG framework to an important signal processing problem: the joint beamforming and compression problem (JBCP) with per-antenna power constraints (PAPCs) in cooperative cellular networks. This customized application requires careful exploitation of the problem’s special structure such as the tightness of the semidefinite relaxation (SDR) and the differentiability of the dual. Numerical experiments demonstrate the superior performance of our custom-application over state-of-the-art benchmarks for the JBCP. © 2025, CC BY.

关键词： Beamforming

Statistical Multiplexing Gain Analysis of Centralized Open Radio Access Networks with Limited Cells and Heterogeneous Traffics

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IEEE Transactions on Vehicular Technology 2025年

作者： Wang, Lu Zhou, Yiqing Liu, Ya-Feng Liu, Ling Shi, Ningzhe Tian, Lin Shi, Jinglin National Key Laboratory of Transient Impact Beijing102202 China 208 Research Institute of China Ordnance Industries Beijing102202 China Chinese Academy of Sciences State Key Lab of Processors Institute of Computing Technology Beijing100190 China University of Chinese Academy of Sciences Beijing100049 China Beijing Key Laboratory of Mobile Computing and Pervasive Device Beijing100190 China Chinese Academy of Sciences State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Beijing100190 China Chinese Academy of Sciences Institute of Computing Technology Beijing100190 China Nanjing Institute of InforSuperBahn Nanjing211100 China

Centralized open radio access networks (O-RANs) aggregate computing resources of multiple cells to improve resource utilization and achieve statistical multiplexing gain (SMG), i.e., the ratio of the number of deployed resources (DepR) for distributed radio access network (D-RAN) to that for O-RAN. SMG of O-RAN has been investigated with infinite number of cells with homogeneous bursty-temporal traffic features. However, in practice, the number of cells is limited, and in the era of Internet of Things (IoT), cells with heterogeneous bursty-temporal traffics (het-traffics), should be considered. This paper analyzes the SMG of O-RAN with limited het-traffic cells. First of all, given traffic models of het-traffic cells following different bursty lognormal distribution and periodic time-varying features, required resources (ReqR) for D-RAN can be derived. Then, to obtain the distribution of ReqR for O-RAN with limited het-traffic cells, a Gaussian mixture model (GMM) based resource distribution approximation (GMM-RDA) is proposed. Thus SMG can be obtained for any given service rate. In simulations, the effectiveness of GMM-RDA is verified by Kolmogorov-Smirnov (K-S) test, and the accuracy of achieved SMG can be up to 99.7%, which is about 33% higher than that obtained by the law of large numbers (LLN) for infinite cells. Moreover, het-traffic cells resulting from service diversification can enhance SMG in O-RAN by 34.7%. © 1967-2012 IEEE.

关键词： Radio access networks

QoS-Based Beamforming and Compression Design for Cooperative Cellular Networks via Lagrangian Duality

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IEEE Transactions on Signal Processing 2025年

作者： Fan, Xilai Liu, Ya-Feng Liu, Liang Chang, Tsung-Hui Chinese Academy of Sciences State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Beijing100190 China The Hong Kong Polytechnic University Department of Electronic and Information Engineering Hong Kong Hong Kong The Chinese University of HongKong School of Science and Engineering Shenzhen Shenzhen China Shenzhen Research Institute of Big Data China

This paper considers the quality-of-service (QoS)-based joint beamforming and compression design problem in the downlink cooperative cellular network, where multiple relay-like base stations (BSs), connected to the central processor via ratelimited fronthaul links, cooperatively transmit messages to the users. The problem of interest is formulated as the minimization of the total transmit power of the BSs, subject to all users' signal-to-interference-plus-noise ratio (SINR) constraints and all BSs' fronthaul rate constraints. In this paper, we first show that there is no duality gap between the considered joint optimization problem and its Lagrangian dual by showing the tightness of its semidefinite relaxation (SDR). Then, we propose an efficient algorithm based on the above duality result for solving the considered problem. The proposed algorithm judiciously exploits the special structure of an enhanced Karush-Kuhn-Tucker (KKT) conditions of the considered problem and approaches the solution that satisfies the enhanced KKT conditions via two fixed point iterations. Two key features of the proposed algorithm are: (1) it is able to detect whether the considered problem is feasible or not and find its globally optimal solution when it is feasible;(2) it is highly efficient because both of the fixed point iterations in the proposed algorithm are linearly convergent and function evaluations in the fixed point iterations are computationally cheap. Numerical results show the global optimality and efficiency of the proposed algorithm. © 1991-2012 IEEE.

关键词： Lagrange multipliers

Joint Design of Radar Receive Filter and Unimodular ISAC Waveform with Sidelobe Level Control

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arXiv 2025年

作者： Zhang, Kecheng Liu, Ya-Feng Wang, Zhongbin Yuan, Weijie Keskin, Musa Furkan Wymeersch, Henk Xia, Shuqiang School of System Design and Intelligent Manufacturing The Shenzhen Key Laboratory of Robotics and Computer Vision Southern University of Science and Technology Shenzhen518055 China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China Department of Electrical Engineering Chalmers University of Technology Gothenburg41296 Sweden ZTE Corporation The State Key Laboratory of Mobile Network and Mobile Multimedia Technology Shenzhen518055 China

Integrated sensing and communication (ISAC) has been considered a key feature of next-generation wireless networks. This paper investigates the joint design of the radar receive filter and dual-functional transmit waveform for the multiple-input multiple-output (MIMO) ISAC system. While optimizing the mean square error (MSE) of the radar receive spatial response and maximizing the achievable rate at the communication receiver, besides the constraints of full-power radar receiving filter and unimodular transmit sequence, we control the maximum range sidelobe level, which is often overlooked in existing ISAC waveform design literature, for better radar imaging performance. To solve the formulated optimization problem with convex and nonconvex constraints, we propose an inexact augmented Lagrangian method (ALM) algorithm. For each subproblem in the proposed inexact ALM algorithm, we custom-design a block successive upper-bound minimization (BSUM) scheme with closed-form solutions for all blocks of variable to enhance the computational efficiency. Convergence analysis shows that the proposed algorithm is guaranteed to provide a stationary and feasible solution. Extensive simulations are performed to investigate the impact of different system parameters on communication and radar imaging performance. Comparison with the existing works shows the superiority of the proposed algorithm. © 2025, CC BY-NC-SA.

关键词： Mean square error

Riemannian Optimization for Holevo Capacity

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arXiv 2025年

作者： Zhu, Chengkai Peng, Renfeng Gao, Bin Wang, Xin Guangzhou China State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China University of Chinese Academy of Sciences Beijing China

computing the classical capacity of a noisy quantum channel is crucial for understanding the limits of communication over quantum channels. However, its evaluation remains challenging due to the difficulty of computing the Holevo capacity and the even greater difficulty of regularization. In this work, we formulate the computation of the Holevo capacity as an optimization problem on a product manifold constructed from probability distributions and their corresponding pure input states for a quantum channel. A Riemannian gradient descent algorithm is proposed to solve the problem, providing lower bounds on the classical capacity of general quantum channels and outperforming existing methods in numerical experiments in both efficiency and scale. © 2025, CC BY.

关键词： Probability distributions

Cascaded adaptive aberration-eliminating multimode fiber imaging

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Advanced Photonics 2025年第02期 135-143页

作者： Zhong Wen Qilin Deng Quanzhi Li Yizhou Tan Jingshan Zhong Chiming Zhang Jiahe Zhang Clemens F.Kaminski Ying Gu Xu Liu Qing Yang Zhejiang University College of Optical Science and Engineering State Key Laboratory of Extreme Photonics and Instrumentation Zhejiang University International Research Center for Advanced Photonics Zhejiang University ZJU-Hangzhou Global Scientific and Technological Innovation Center Chinese PLA General Hospital The First Medical Center Department of Laser Medicine Chinese PLA General Hospital Hainan HospitalLaser Medicine Center Zhejiang Laboratory Research Center for Intelligent Manufacturing Computing University of Cambridge Department of Chemical Engineering and Biotechnology

In vivo microscopic imaging inside a biological lumen such as the gastrointestinal tract, respiratory airways, or within blood vessels has faced significant technological challenges for decades. A promising candidate technology is the multimode fiber(MMF) endoscope, which enables minimally invasive diagnostics at a resolution reaching the cellular level. However, for in vivo imaging applications deep inside a biological lumen, sample-induced aberrations and the dynamic dispersion in the MMF make the MMF endoscope a chaotic system with many unknowns, where multiple minor fluctuations can couple and compound into intractable problems. We introduce a dynamically encoding, cascaded, optical, and ultrathin polychromatic light-field endoscopy(DECOUPLE) to tackle this challenge. DECOUPLE includes an adaptive aberration correction that can accurately track and control MMF behavior in the spatial-frequency domain to compensate for chaos introduced during complex dynamic imaging processes. We demonstrate the flexibility and practicality of DECOUPLE for noninvasive volumetric imaging in two colors for light passing through various highly aberrating samples including 120-μm-thick onion epidermal slices and 80-μm-thick layers of fat emulsions. To summarize, we represent a significant step toward practical in vivo imaging deep within biological tissue.

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The Distributionally Robust Optimization Model of Sparse Principal Component Analysis

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arXiv 2025年

作者： Wang, Lei Liu, Xin Chen, Xiaojun Department of Applied Mathematics The Hong Kong Polytechnic University Hong Kong State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences University of Chinese Academy of Sciences Beijing China

We consider sparse principal component analysis (PCA) under a stochastic setting where the underlying probability distribution of the random parameter is uncertain. This problem is formulated as a distributionally robust optimization (DRO) model based on a constructive approach to capturing uncertainty in the covariance matrix, which constitutes a nonsmooth constrained min-max optimization problem. We further prove that the inner maximization problem admits a closed-form solution, reformulating the original DRO model into an equivalent minimization problem on the Stiefel manifold. This transformation leads to a Riemannian optimization problem with intricate nonsmooth terms, a challenging formulation beyond the reach of existing algorithms. To address this issue, we devise an efficient smoothing manifold proximal gradient algorithm. We prove the Riemannian gradient consistency and global convergence of our algorithm to a stationary point of the nonsmooth minimization problem. Moreover, we establish the iteration complexity of our algorithm. Finally, numerical experiments are conducted to validate the effectiveness and scalability of our algorithm, as well as to highlight the necessity and rationality of adopting the DRO model for sparse PCA. Copyright © 2025, The Authors. All rights reserved.

关键词： Optimization algorithms