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Cosmological perturbations in the energy-momentum squared gravity theory:constraints from gravitational wave standard sirens and redshift space distortions

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Chinese Physics C 2025年第4期49卷 199-208页

作者： Qi-Ming Fu Xin Zhang Institute of Physics Shaanxi University of TechnologyHanzhong 723000China Lanzhou Center for Theoretical Physics Key Laboratory of Theoretical Physics of Gansu Provinceand Key Laboratory of Quantum Theory and Applications of MoELanzhou UniversityLanzhou 730000China Key Laboratory of Cosmology and Astrophysics(Liaoning)&College of Sciences Northeastern UniversityShenyang 110819China Key Laboratory of Data Analytics and Optimization for Smart Industry(Ministry of Education) Northeastern UniversityShenyang 110819China National Frontiers Science Center for Industrial Intelligence and Systems Optimization Northeastern UniversityShenyang 110819China

We investigate the linear cosmological perturbations in the context of the so-called energy-momentum squared gravity(EMSG)*** research shows that the EMSG theory can reproduce a viable background cosmological evolution comparable toΛCDM,whereas the matter-dominated era exhibits slight *** this paper,we focus on power-law EMSG models and derive the equations for the linear cosmological *** explore the propagation of the gravitational wave(GW)and the growth of matter density perturbation at the first order,and we estimate the model parameters from the simulated GW and observed redshift space distortion *** analysis reveals that the model parameters should be small and positive in the confidence interval,which indicates that the theory agrees closely with the observational data and can be considered an alternative to the standard cosmological model.

关键词： energy-momentum squared gravity cosmological perturbations gravitational wave cosmological parameters

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STABLE RECOVERY OF SPARSE SIGNALS WITH NON-CONVEX WEIGHTED r-NORM MINUS 1-NORM

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Journal of Computational Mathematics 2025年第1期43卷 43-62页

作者： Jianwen Huang Feng Zhang Xinling Liu Jianjun Wang Jinping Jia Runke Wang School of Mathematical Sciences Chongqing Normal UniversityChongqing 401331China School of Mathematics and Statistics Tianshui Normal UniversityTianshui 741001China chool of Mathematics and Statistics Southwest UniversityChongqing 400715China Key Laboratory of Optimization Theory and Applications at China West Normal University of Sichuan Province School of Mathematics and InformationChina West Normal UniversityNanchong 637009China School of Mathematics and Statistics Southwest UniversityChongqing 400715China School of Mathematics and Information Science North Minzu UniversityYinchuan 750021China College of Resources and Environmental Engineering Tianshui Normal UniversityTianshui 741001China

Given the measurement matrix A and the observation signal y,the central purpose of compressed sensing is to find the most sparse solution of the underdetermined linear system y=Ax+z,where x is the s-sparse signal to be recovered and z is the noise *** and Yu[***.,5(2019),Article 14]recently proposed a novel non-convex weighted l_(r)-l_(2)minimization method for effective sparse *** this paper,under newly coherence-based conditions,we study the non-convex weighted l_(r)-l_(2)minimization in reconstructing sparse signals that are contaminated by different ***,the results reveal that if the coherenceμof measurement matrix A fulfillsμ1,α^(1/r)N(1/2)<1,then any s-sparse signals in the noisy scenarios could be ensured to be reconstructed robustly by solving weighted l_(r)-l_(2)minimization non-convex optimization ***,some central remarks are presented to clear that the reconstruction assurance is much weaker than the existing *** the best of our knowledge,this is the first mutual coherence-based sufficient condition for such approach.

关键词： Compressed sensing Sparse recovery Mutual coherence Sufficient condition

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Resource Allocation for Underwater Acoustic Sensor Networks With Partial Spectrum Sharing: When optimization Meets Deep Reinforcement Learning

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IEEE Transactions on Network and Service Management 2025年

作者： Tang, Rui Zhang, Ruizhi Xu, Yongjun Liu, Chuan Huang, Chongwen Yuen, Chau China West Normal University School of Electronic Information Engineering Nanchong637002 China China West Normal University of Sichuan Province Key Laboratory of Optimization Theory and Applications Nanchong637002 China Internet of Things Perception and Big Data Analysis Key Laboratory of Nanchong City Nanchong637002 China University of Electronic Science and Technology of China School of Information and Communication Engineering Chengdu611731 China Chongqing University of Posts and Telecommunications School of Communications and Information Engineering Chongqing400064 China Zhejiang University College of Information Science and Electronic Engineering Hangzhou310027 China Nanyang Technological University School of Electrical and Electronics Engineering Singapore639798 Singapore

To utilize the limited acoustic spectrum while combating the harsh underwater propagation, we incorporate partial spectrum sharing into an underwater acoustic sensor network and aim to maximize the minimum data collection rate among all underwater sensor nodes through joint power allocation and spectrum assignment. To cope with the non-convex optimization problem, we propose a Hybrid Model-based and Data-based Resource Allocation (HMDRA) scheme: 1) Under any given spectrum assignment strategy, we analyze the impact of the partial spectrum sharing and imperfect successive interference cancellation on baseband signal processing, and formulate a power allocation problem that is solved by the bisection method and Lagrange dual theory. 2) Based on the optimal power allocation strategy, the gradient-free genetic algorithm (GA) is first adopted to approach the optimal solution of the model-less spectrum assignment problem by nearly enumerating the solution space. To reduce complexity, we further propose a deep reinforcement learning (DRL)-based algorithm and obtain an efficient solution by traversing a deep neural network-based policy learned from the training stage. Simulation results show that compared with the GA-based algorithm, the average execution time of the DRL-based algorithm is substantially reduced by 5 orders of magnitude to 0.7076 seconds at the cost of approximately 6 percent performance loss. © 2004-2012 IEEE.

关键词： Deep reinforcement learning

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Iterative natural thresholding algorithm for seismic inversion aimed at potentially recovering geological interfaces characterized by weak reflection

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Journal of Asian Earth Sciences: X 2025年 13卷

作者： Zidan Fan Ronghuo Dai Yue Feng School of Mathematics and Information China West Normal University Nanchong Sichuan China Sichuan Colleges and Universities Key Laboratory of Optimization Theory and Applications China West Normal University Nanchong Sichuan China Institute of Nonlinear Analysis and Applications China West Normal University Nanchong Sichuan China

Seismic inversion has developed into the core technology of quantitative prediction of rock’s elastic properties of underground in the exploration geophysics. In practical application, seismic impedance inversion is a frequently utilized technique. But it still has unsatisfactory protection of small reflectivity series in real seismic data. These small reflectivity series correspond to the weak reflections of geological interfaces, which is usually a sign of low acoustic impedance contrast in tunnels engineering or reservoirs of oil and gas in petroleum engineering, and other strata of geological significance. Hence, it is very important and meaningful to recover them from original seismic data. This paper adopts a novel algorithm named iterative natural thresholding algorithm (INTA) with the aim to improve the protection of weak reflections. Through an optimal thresholding operator and a concave regularization to enforce an optimal sparse solution, INTA can potentially recover these geological interfaces characterized by weak reflection. We utilize a synthetic seismic data profile and a real seismic data set to test its feasibility and show its better protection of small reflectivity series. From the inversion results, one can see that, compared to common used sparse constrained seismic inversion method, the inverted impedance by the proposed method can better characterize weak reflectors and help understand the structure of the earth more accurately.

关键词： Seismic inversion Impedance Natural thresholding algorithm L0-norm Weak reflection

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Convergence of Bregman Alternating Direction Method of Multipliers for Nonseparable Nonconvex Objective with Linear Constraints

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Journal of Applied Mathematics and Physics 2024年第2期12卷 639-660页

作者： Xiaotong Zeng Junping Yao Haoming Xia Key Laboratory of Optimization Theory and Applications School of Mathematics and Information China West Normal University Nanchong China

In this paper, our focus lies on addressing a two-block linearly constrained nonseparable nonconvex optimization problem with coupling terms. The most classical algorithm, the alternating direction method of multipliers (ADMM), is employed to solve such problems typically, which still requires the assumption of the gradient Lipschitz continuity condition on the objective function to ensure overall convergence from the current knowledge. However, many practical applications do not adhere to the conditions of smoothness. In this study, we justify the convergence of variant Bregman ADMM for the problem with coupling terms to circumvent the issue of the global Lipschitz continuity of the gradient. We demonstrate that the iterative sequence generated by our approach converges to a critical point of the issue when the corresponding function fulfills the Kurdyka-Lojasiewicz inequality and certain assumptions apply. In addition, we illustrate the convergence rate of the algorithm.

关键词： Nonseparable Nonconvex optimization Bregman ADMM Kurdyka-Lojasiewicz Inequality

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Almost Sure Convergence of Proximal Stochastic Accelerated Gradient Methods

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Journal of Applied Mathematics and Physics 2024年第4期12卷 1321-1336页

作者： Xin Xiang Haoming Xia Key Laboratory of Optimization Theory and Applications School of Mathematics and Information China West Normal University Nanchong China

Proximal gradient descent and its accelerated version are resultful methods for solving the sum of smooth and non-smooth problems. When the smooth function can be represented as a sum of multiple functions, the stochastic proximal gradient method performs well. However, research on its accelerated version remains unclear. This paper proposes a proximal stochastic accelerated gradient (PSAG) method to address problems involving a combination of smooth and non-smooth components, where the smooth part corresponds to the average of multiple block sums. Simultaneously, most of convergence analyses hold in expectation. To this end, under some mind conditions, we present an almost sure convergence of unbiased gradient estimation in the non-smooth setting. Moreover, we establish that the minimum of the squared gradient mapping norm arbitrarily converges to zero with probability one.

关键词： Proximal Stochastic Accelerated Method Almost Sure Convergence Composite optimization Non-Smooth optimization Stochastic optimization Accelerated Gradient Method

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Manifold learning localization based on local tangent space alignment for wireless sensor networks

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International Journal of Computers and applications 2024年第9期46卷 785-794页

作者： Zhang, Hanyu Xu, Hao School of Mathematics and Information China West Normal University Nanchong China Key Laboratory of Optimization Theory and Applications at China West Normal University of Sichuan Province Nanchong China

At present, nodes localization in wireless sensor networks are one of the focuses of many scholars' research. But now the current localization algorithms usually face the problems of low localization accuracy and high computation. Since the information captured by wireless sensor networks is essentially nonlinear, thus this paper proposes a localization algorithm based on manifold learning algorithm local tangent space alignment for wireless sensor networks. It can process nonlinear data to achieve good positioning effect, and the variables in the algorithm have little impact on the localization effect. Two types of positioning data are considered for localization: the measurement distance and the signal strength between sensor nodes. Firstly, the local k-neighborhoods of the localized data points can be found for determining the low-dimensional geometric structure of their local tangent spaces by principal component analysis. Next, the local tangent space of the localized sample points is aligned to obtain the relative locations of the sensor nodes. Then, the physical locations of the sensor nodes can be get by lining up the relative positions with anchor points. Finally, the ending of the paper by doing simulation experiments demonstrate that the algorithm has good precision and few variables in performing nodes localization. © 2024 Informa UK Limited, trading as Taylor & Francis Group.

关键词： Sensor nodes

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ACCELERATED SYMMETRIC ADMM AND ITS applications IN LARGE-SCALE SIGNAL PROCESSING

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Journal of Computational Mathematics 2024年第6期42卷 1605-1626页

作者： Jianchao Bai Ke Guo Junli Liang Yang Jing H.C.So Research&Development Institute of Northwestern Polytechnical University in Shenzhen Shenzhen 518057China School of Mathematics and Statistics Northwestern Polytechnical UniversityXi’an 710129China Key Laboratory of Optimization Theory and Applications at China West Normal University of Sichuan Province School of Mathematics and InformationChina West Normal UniversityNanchong 637009China School of Electronics and Information Northwestern Polytechnical UniversityXi’an 710129China Department of Electrical Engineering City University of Hong KongHong KongSARChina

The alternating direction method of multipliers(ADMM)has been extensively investigated in the past decades for solving separable convex optimization problems,and surprisingly,it also performs efficiently for nonconvex *** this paper,we propose a symmetric ADMM based on acceleration techniques for a family of potentially nonsmooth and nonconvex programming problems with equality constraints,where the dual variables are updated twice with different *** proper assumptions instead of the socalled Kurdyka-Lojasiewicz inequality,convergence of the proposed algorithm as well as its pointwise iteration-complexity are analyzed in terms of the corresponding augmented Lagrangian function and the primal-dual residuals,*** of our algorithm is verified by numerical examples corresponding to signal processing applications in sparse nonconvex/convex regularized minimization.

关键词： Nonconvex optimization Symmetric ADMM Acceleration technique Complexity Signal processing

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A Tabu Search Algorithm Based on Population Search Framework for Solving Multi-Budget Maximum Coverage Problem

SSRN

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SSRN 2023年

作者： Liu, Yawen Pan, Dazhi School of Mathematics and Information China West Normal University Nanchong637009 China Sichuan Colleges Universities Key Laboratory of Optimization Theory and Applications Nanchong637009 China

The multi-budget maximum coverage problem (MMCP) is a natural and practical expansion of both the budget maximum coverage problem (BMCP) and multiple knapsack problem (MKP), involving k budgets, elements with positive profits, and subsets with non-negative costs. The objective of the MMCP is to maximize the total profit of the elements covered by the budgets. This paper examines the utilization of a tabu search algorithm to the MMCP. By establishing a mathematical model, an evolutionary algorithm is employed as a possible solution method. A population search framework based on tabu search algorithm (PSFBTS) is presented as an innovative and effective technique for solving the MMCP. PSFBTS comprises three essential components that are seamlessly integrated into the population search framework, including selecting promising subsets from restricted neighborhood structures, selecting neighborhood solutions with added perturbations, and generating offspring solutions based on population information exchange. To evaluate the effectiveness of PSFBTS, we performed computations on 30 benchmark instances of the extended BMCP, and compared the results with the greedy algorithm, genetic algorithm, particle swarm optimization algorithm, and CPLEX solver. The experimental results demonstrate that PSFBTS not only performs efficiently, but also yields solutions of superior quality. © 2023, The Authors. All rights reserved.

关键词： Profitability

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Existence of Weak Pareto Efficient Solutions of a Vector optimization Problem under a Closed Constraint Set

arXiv

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arXiv 2024年

作者： Liu, Danyang Li, Jun Mastroeni, Giandomenico Key Laboratory of Optimization Theory and Applications China West Normal University of Sichuan Province School of Mathematics and Information China West Normal University Sichuan Nanchong637009 China Department of Computer Science University of Pisa Largo B. Pontecorvo 3 Pisa56127 Italy

In this paper, we investigate the nonemptiness of weak Pareto efficient solution set for a class of nonsmooth vector optimization problems on a nonempty closed constraint set without any boundedness and convexity assumptions. First, we obtain a new property concerning the nonemptiness of weak Pareto efficient solution sets for these vector optimization problems. Then, under the condition of weak section-boundedness from below, we establish relationships between the notions of properness, Palais-Smale, weak Palais-Smale and M-tameness conditions with respect to some index sets for the restriction of the vector mapping on the constraint set. Finally, we present some new necessary and sufficient conditions for the nonemptiness of the weak Pareto efficient solution set for a general class of nonsmooth vector optimization problems. Copyright © 2024, The Authors. All rights reserved.

关键词： Vectors

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