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Alternative structured spectral gradient algorithms for solving nonlinear least-squares problems

HELIYON 2021年第7期7卷 e07499页

作者： Yahaya, Mahmoud Muhammad Kumam, Poom Awwal, Aliyu Muhammed Aji, Sani King Mongkuts Univ Technol Thonburi KMUTT Fac Sci Dept Math Ctr Excellence Theoret & Computat Sci TaCS CoE 126 Pracha Uthit Rd Bangkok 10140 Thailand King Mongkuts Univ Technol Thonburi KMUTT Fac Sci Dept Math KMUTTFixed Point Res Lab 126 Pracha Uthit RdRoom SCL 802 Fixed Point Lab Bangkok 10140 Thailand King Mongkuts Univ Technol Thonburi KMUTT Fac Sci Ctr Excellence Theoret & Computat Sci TaCS CoE BNCAO Res CtrFixed Point Theory & Applicat Res G 126 Pracha Uthit Rd Bangkok 10140 Thailand King Mongkuts Univ Technol Thonburi Fac Sci Dept Math 126 Pracha Uthit Rd Bangkok 10140 Thailand Gombe State Univ Fac Sci Dept Math Gombe 760214 Nigeria

The study of efficient iterative algorithms for addressing nonlinear least-squares (NLS) problems is of great importance. The NLS problems, which belong to a special class of unconstrained optimization problems, are of particular interest because of the special structure of their gradients and Hessians. In this paper, based on the spectral parameters of Barzillai and Borwein (1998), we propose three structured spectral gradient algorithms for solving NLS problems. Each spectral parameter in the respective algorithms incorporates the structured gradient and the information gained from the structured Hessian approximation. Moreover, we develop a safeguarding technique for the first two structured spectral parameters to avoid negative curvature directions. Moreso, using a nonmonotone line-search strategy, we show that the proposed algorithms are globally convergent under some standard conditions. The comparative computational results on some standard test problems show that the proposed algorithms are efficient.

关键词： iterative algorithm Spectral gradient algorithm Nonlinear least squares Line-search Quasi-Newton algorithm

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MuSP: A multistep screening procedure for sparse recovery

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STAT 2021年第1期10卷

作者： Yang, Yuehan Zhu, Ji George, Edward, I Cent Univ Finance & Econ Dept Stat Beijing 100081 Peoples R China Univ Michigan Dept Stat Ann Arbor MI 48109 USA Univ Penn Wharton Sch Dept Stat Philadelphia PA 19104 USA

We propose a multistep screening procedure (MuSP) for the recovery of sparse linear models in high-dimensional data. This method is based on a repeated small penalty strategy that quickly converges to an estimate within a few iterations. Specifically, in each iteration, an adaptive lasso regression with a small penalty is fit within the reduced feature space obtained from the previous step, rendering its computational complexity roughly comparable with the Lasso. MuSP is shown to select the true model under complex correlation structures among the predictors and response, even when the irrepresentable condition fails. Further, under suitable regularity conditions, MuSP achieves the optimalminimax rate (q log n/n)(1/2) for the upperbound of l(2)-norm error. Numerical comparisons show that the method works effectively both in model selection and estimation, and the MuSP fitted model is stable over a range of small tuning parameter values, eliminating the need to choose the tuning parameter by cross-validation. We also apply MuSP to financial data and show that MuSP is successful in asset allocation selection.

关键词： high-dimensional data iterative algorithm Lasso multistep method

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A kernel-free quadratic surface twin support vector machine with capped L1-norm distance metric for robust classification

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Applied Soft Computing 2025年 180卷

作者： Si, Qi Yang, Zhixia Zhao, Jinbiao Chen, Rongda College of Mathematics and Systems Science Xinjiang University Urumuqi China Institute of Mathematics and Physics Xinjiang University Urumuqi China School of Computer Science and Information Engineering Hefei University of Technology Hefei China College of Education Dehong Teachers’ College Dehong China

In this paper, we propose a robust capped L1-norm kernel-free quadratic surface twin support vector machine (CL1QTSVM) for robust classification tasks. By incorporating the capped L1-norm distance metric and adopting a kernel-free approach, the CL1QTSVM not only enhances robustness against outliers but also eliminates the need for selecting kernel functions and tuning their parameters, significantly saving computational time. The introduction of an L2-norm regularization term further ensures that the model adheres to structural risk minimization, thus improving its generalization ability. The primal non-differentiable optimization problems are equivalently reformulated into a pair of differentiable problems using re-weighting techniques and vectorization operators. An efficient alternating iteration algorithm is developed based on these reformulations. Additionally, the dimensionality of the inverse matrix is effectively reduced in high-dimensional feature spaces by applying the Sherman–Morrison–Woodbury formula. Theoretical analyses are provided on the convergence properties, time complexity, and the existence of locally optimal solutions to the optimization problems. Extensive experiments on several benchmark datasets validate the classification performance and robustness of the proposed model.

关键词： Capped L1-norm iterative algorithm Kernel-free technique Robust classification Twin support vector machine

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Estimation method of cable tension based on iterative algorithm and optimization algorithm

Estimation method of cable tension based on iterative algori...

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3rd International Conference on Civil Engineering, Architecture and Building Materials (CEABM 2013)

作者： Huang, Yong-hui Luo, De-quan Rao, Rui Guangzhou Univ Guangzhou Univ Tamkang Univ Joint Res Ctr Engn St Guangzhou 510006 Guangdong Peoples R China South China Univ Technol Sch Civil Engn & Transportat Guangzhou 510640 Peoples R China

ISBN: (纸本)9783037857755

The vibration method is usually used for field measurement of cable tension of cable system bridges. The cable tension evaluation method is mostly based on the simple taut string theory. However, the simple theory may cause unacceptable errors in many applications especially for the cables with big bending stiffness and two ends fixed boundary conditions. In this paper a cable tension estimation method based on iterative algorithm and optimization algorithm is presented and implemented using finite element method and ANSYS soft ware. Compared with the analytical method and empirical formulas the method presented in this paper is more convenient and the application range is more extensive. The accuracy of the method has been verified by a set of test. In the end, the method is used to estimate the cable tension of a tied-arch bridge's suspenders.

关键词： Cable tension estimation frequency method iterative algorithm optimization algorithm

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iterative criteria for identifying strong H-tensors

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2019年 352卷 93-109页

作者： Huang, Baohua Ma, Changfeng Fujian Normal Univ Coll Math & Informat Fuzhou 350117 Fujian Peoples R China Fujian Normal Univ FJKLMAA Fuzhou 350117 Fujian Peoples R China

Strong H-tensors play an important role in the theories and applications of numerical linear algebra. It is necessary to identify whether a given tensor is a strong H-tensor or not. In this paper, we establish some iterative criteria for identifying strong H-tensors. These criteria depend on the elements of the tensors: therefore, they are easy to be verified. The results obtained in this paper extend the corresponding conclusions for strictly generalized diagonally dominant matrices. As an application, some sufficient conditions for the positive definiteness of an even-order real symmetric tensor are presented. Some numerical experiments show the feasibility and efficiency of the results which are obtained in this paper. (C) 2018 Elsevier B.V. All rights reserved.

关键词： Strong H-tensors Strictly generalized diagonally dominant iterative algorithm Positive definiteness Numerical experiments

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An iterative algorithm for Differentially Private Histogram Publication

An Iterative Algorithm for Differentially Private Histogram ...

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International Conference on Cloud Computing and Big Data (CLOUDCOM-ASIA)

作者： Chen, Hong Wu, Yingjie Chen, Tingting Wang, Xiaodong Fuzhou Univ Coll Math & Comp Sci Fuzhou 350108 Peoples R China

ISBN: (纸本)9781479928293

Traditionally, the accuracy of range queries in differentially private histogram publication was boosted by obtaining the Best Linear Unbiased Estimator (BLUE) of the nodes' noisy values in the Differential Privacy Range Tree (DPRT). However, exist works require DPRT be perfect k-ary, which means it is not suitable for differentially private histogram publication under arbitrary tree structure In this paper, we propose an efficient iterative algorithm GBLUE for differential privacy histogram publication based on any tree structure. The correctness of GBLUE is guaranteed by theoretical analysis and experimental demonstration. Experimental results show that GBLUE is effective and feasible.

关键词： differential privacy iterative algorithm histogram publication

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iterative solution of Helmert transformation based on a unit dual quaternion

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ACTA GEODAETICA ET GEOPHYSICA 2019年第1期54卷 123-141页

作者： Zeng, Huaien Chang, Guobin He, Haiqing Tu, Yi Sun, Shuifa Wu, Yue China Three Gorges Univ Natl Field Observat & Res Stn Landslides Three Go Yichang 443002 Peoples R China China Three Gorges Univ Hubei Key Lab Intelligent Vis Based Monitoring Hy Yichang 443002 Peoples R China China Three Gorges Univ Hubei Key Lab Construct & Management Hydropower E Yichang 443002 Peoples R China China Univ Min & Technol Sch Environm Sci & Spatial Informat Xuzhou 221116 Jiangsu Peoples R China East China Univ Technol Sch Geomat Nanchang 330013 Jiangxi Peoples R China China Three Gorges Univ Key Lab Geol Hazards Three Gorges Reservoir Area Minist Educ Yichang 443002 Peoples R China

The rigid motion involving both rotation and translation in the 3D space can be simultaneously described by a unit dual quaternion. Considering this excellent property, the paper constructs the Helmert transformation (seven-parameter similarity transformation) model based on a unit dual quaternion and then presents a rigid iterative algorithm of Helmert transformation using a unit dual quaternion. Because of the singularity of the coefficient matrix of the normal equation, the nine parameter (including one scale factor and eight parameters of a dual quaternion) Helmert transformation model is reduced into five parameter (including one scale factor and four parameters of a unit quaternion which can represent the rotation matrix) Helmert transformation one. Besides, a good start estimate of parameter is required for the iterative algorithm, hence another algorithm employed to compute the initial value of parameter is put forward. The numerical experiments involving a case of small rotation angles i.e. geodetic coordinate transformation and a case of big rotation angles i.e. the registration of LIDAR points are studied. The results show the presented algorithms in this paper are correct and valid for the two cases, disregarding the rotation angles are big or small. And the accuracy of computed parameter is comparable to the classic Procrustes algorithm from Grafarend and Awange (J Geod 77:66-76, 2003), the orthonormal matrix algorithm from Zeng (Earth Planets Space 67:105, 2015), and the algorithm from Wang et al.

关键词： Helmert transformation Dual quaternion iterative algorithm Initial value of parameter Geodetic coordinate transformation

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A Current-Driven Six-Channel Potentiostat for Rapid Performance Characterization of Microbial Electrolysis Cells

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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT 2019年第12期68卷 4694-4702页

作者： Molderez, Tom R. Zhang, Xu Rabaey, Korneel Verhelst, Marian Katholieke Univ Leuven Dept Elect Engn ESAT MICAS B-3000 Leuven Belgium Univ Ghent Ctr Microbial Ecol & Technol B-9000 Ghent Belgium

Knowledge of the performance of microbial electrolysis cells under a wide range of operating conditions is crucial to achieve high production efficiencies. Characterizing this performance in an experiment, however, is challenging due to either the long measurement times of steady-state procedures or the transient errors of dynamic procedures. Moreover, wide parallelization of the measurements is not feasible due to the high measurement equipment cost per channel. Hence, to speedup this characterization and to facilitate low-cost, yet widely parallel measurements, this paper presents a novel rapid polarization curve measurement procedure with a dynamic measurement resolution that runs on a custom six-channel potentiostat with a current-driven topology. As case study, the procedure is used to rapidly assess the impact of altering pH values on a microbial electrolysis cell that produces H-2. A $\times 2$ - $\times 12$ speedup could be obtained in comparison with the state-of-the-art, depending on the characterization resolution (16-128 levels). On top of this speedup, measurements can be parallelized up to $6\times $ on the presented, affordable-42-per-channel-potentiostat.

关键词： Analog circuits bioelectric phenomena closed-loop systems electrochemical devices iterative algorithm measurement microorganisms PI-control real-time systems search methods

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Robust reconstruction of fluorescence molecular tomography by minimizing the capped L2,p norm

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BIOMEDICAL SIGNAL PROCESSING AND CONTROL 2025年 109卷

作者： Yuan, Yating Guo, Hongbo Yu, Jingjing Yi, Huangjian He, Xuelei He, Xiaowei Xian Key Lab Radiom & Intelligent Percept Xian Peoples R China Northwest Univ Sch Informat Sci & Technol Xian 710127 Peoples R China Shaanxi Normal Univ Sch Phys & Informat Technol Xian 710119 Peoples R China

Fluorescence molecular tomography (FMT) is a promising imaging modality capable of reconstructing the three-dimensional spatial distribution of interior fluorescent targets. Several compressed sensing (CS)-based methods have been proposed for reconstruction. However, these methods perform poorly in the presence of noise, as they typically employ the squared L2 norm to measure reconstruction errors, which amplifies the negative impact of noise and compromises robustness. To address this issue, we propose a robust reconstruction model based on the capped L2,p norm metric, which retains the advantages of CS while enhancing robustness against noise. The capped L2,p norm extends traditional metrics by introducing the parameter p and a capping threshold, effectively limiting the influence of large errors. Moreover, it provides greater robustness than conventional L2 and L1 norms by adaptively truncating extreme values. As a result, the proposed model effectively suppresses noise and outliers, leading to improved reconstruction stability. The established reconstruction model is nonsmooth and nonconvex due to the capped L2,p norm. To optimize it efficiently, we introduce an iterative re-weighted algorithm, termed CIRWA. Additionally, the convergence of the algorithm is theoretically analyzed. Numerical simulations and in vivo experiments are conducted to validate the performance of CIRWA. The results demonstrate that, compared with state-of-the-art methods, CIRWA achieves more accurate fluorescent target reconstruction and exhibits superior robustness. These findings suggest that CIRWA has significant potential to advance the preclinical applications of FMT.

关键词： Fluorescence molecular tomography p norm Robustness iterative algorithm

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DC-Bias and Power Allocation in Cooperative VLC Networks for Joint Information and Energy Transfer

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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 2019年第12期18卷 5486-5499页

作者： Obeed, Mohanad Dahrouj, Hayssam Salhab, Anas M. Zummo, Salam A. Alouini, Mohamed-Slim King Fahd Univ Petr & Minerals Dept Elect Engn Dhahran 31261 Saudi Arabia Effat Univ Dept Elect Engn Jeddah 21478 Saudi Arabia King Abdullah Univ Sci & Technol Dept Comp Elect & Math Sci & Engn Thuwal 23955 Saudi Arabia

Visible light communications (VLC) have emerged as a strong candidate for meeting the escalating demand for high data rates. In this paper, we consider a VLC network, where multiple access points (APs) serve both energy-harvesting users (EHUs), i.e., users who harvest energy from light emitted by diodes and information users (IUs), i.e., users who gather data information. In order to jointly balance the achievable sum rate at the IUs and the energy harvested by the EHUs, the paper considers maximizing a network-wide utility, which consists of a weighted sum of the IUs sum rate and the EHUs harvested energy, subject to individual IU rate constraint, individual EHU harvested-energy constraint, and AP power constraints, so as to jointly determine the direct current (DC) bias value at each AP, and the power of the alternating-current (AC) signals of the users. A difficult non-convex optimization problem is solved using an iterative approach which relies on inner convex approximations, and compensates for the used approximations using proper outer-loop updates. The paper further considers solving the special cases of the problem, i.e., maximizing the sum rate, and maximizing the total harvested-energy, both subject to the same constraints. Numerical results highlight the significant performance improvement of the proposed algorithms, and illustrate the impacts of the network parameters on the performance trade-off between the sum rate and harvested-energy.

关键词： Visible light communication energy harvesting sum rate DC bias iterative algorithm

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