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Riemannian Newton and trust-region algorithms for analytic rotation in exploratory factor analysis

BRITISH JOURNAL OF MATHEMATICAL & STATISTICAL PSYCHOLOGY 2021年第1期74卷 139-163页

作者： Liu, Yang Univ Maryland Dept Human Dev & Quantitat Methodol 12308 Benjamin Bldg3942 Campus Dr College Pk MD 20742 USA

In exploratory factor analysis, latent factors and factor loadings are seldom interpretable until analytic rotation is performed. Typically, the rotation problem is solved by numerically searching for an element in the manifold of orthogonal or oblique rotation matrices such that the rotated factor loadings minimize a pre-specified complexity function. The widely used gradient projection (GP) algorithm, although simple to program and able to deal with both orthogonal and oblique rotation, is found to suffer from slow convergence when the number of manifest variables and/or the number of latent factors is large. The present work examines the effectiveness of two Riemannian second-order algorithms, which respectively generalize the well-established truncated Newton and trust-region strategies for unconstrained optimization in Euclidean spaces, in solving the rotation problem. When approaching a local minimum, the second-order algorithms usually converge superlinearly or even quadratically, better than first-order algorithms that only converge linearly. It is further observed in Monte Carlo studies that, compared to the GP algorithm, the Riemannian truncated Newton and trust-region algorithms require not only much fewer iterations but also much less processing time to meet the same convergence criterion, especially in the case of oblique rotation.

关键词： exploratory factor analysis analytic rotation Riemannian optimization matrix manifold truncated Newton algorithm trust-region algorithm conjugate gradient algorithm gradient projection algorithm gradient descent algorithm

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Minimum transmission delay algorithm for multi-hop nodes in Internet of Things based on symmetric algorithm

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JOURNAL OF AMBIENT INTELLIGENCE AND HUMANIZED COMPUTING 2020年 1-10页

作者： Hu, Chengbo Liu, Yang Tao, Fengbo Lu, Yongling Wang, Zhen State Grid Jiangsu Elect Power Co Ltd Res Inst Nanjing Peoples R China Southeast Univ Sch Elect Engn Nanjing Peoples R China State Grid Jiangsu Elect Power Co Ltd Dept Technol Nanjing Peoples R China

In view of the increase of network information transmission times, the transmission delay of multi hop nodes in the Internet of Things increases, resulting in the decline of network information transmission performance. In order to improve the quality and performance of information transmission, a minimum transmission delay algorithm of multi-hop nodes in the Internet of Things is designed based on symmetric algorithm. In the perception layer of the Internet of Things, based on the revocable symmetric encryption algorithm, the multi-hop nodes in the perception layer are encrypted;The link information transmission delay under the direct transmission, cooperative transmission and multi-hop transmission modes is compared, and the gradient projection algorithm is used to solve the problem of minimizing the delay of multi-hop nodes' information transmission in the Internet of Things. After calculating the projection matrix and the gradient, the iteration terminates when the steady link traffic and the delay value are obtained. The source node refers to the network node that acts as the source to send the original data packet;the source node uses this algorithm to select the transmission mode with minimum delay, and sends information to the destination node step by step. The simulation test shows that the algorithm can guarantee the security of data transmission of multi-hop nodes in the Internet of Things, and the transmission delay is the minimum.

关键词： Symmetric algorithm Internet of Things Multi-hop nodes gradient projection algorithm Transmission delay algorithm

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A self-adaptive gradient projection algorithm for the nonadditive traffic equilibrium problem

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COMPUTERS & OPERATIONS RESEARCH 2012年第2期39卷 127-138页

作者： Chen, Anthony Zhou, Zhong Xu, Xiangdong Utah State Univ Dept Civil & Environm Engn Logan UT 84322 USA Citilabs Tallahassee FL 32303 USA

gradient projection (GP) algorithm has been shown as an efficient algorithm for solving the traditional traffic equilibrium problem with additive route costs. Recently, GP has been extended to solve the nonadditive traffic equilibrium problem (NaTEP), in which the cost incurred on each route is not just a simple sum of the link costs on that route. However, choosing an appropriate stepsize, which is not known a priori, is a critical issue in GP for solving the NaTEP. Inappropriate selection of the stepsize can significantly increase the computational burden, or even deteriorate the convergence. In this paper, a self-adaptive gradient projection (SAGP) algorithm is proposed. The self-adaptive scheme has the ability to automatically adjust the stepsize according to the information derived from previous iterations. Furthermore, the SAGP algorithm still retains the efficient flow update strategy that only requires a simple projection onto the nonnegative orthant. Numerical results are also provided to illustrate the efficiency and robustness of the proposed algorithm. Published by Elsevier Ltd.

关键词： Traffic equilibrium problem Nonadditive route cost gradient projection algorithm Self-adaptive scheme

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An efficient algorithm for solving the nonnegative tensor least squares problem

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NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS 2021年第6期28卷

作者： Duan, Xue-Feng Duan, Shan-Qi Li, Juan Li, Jiao-fen Wang, Qing-Wen Guilin Univ Elect Technol Guangxi Coll & Univ Key Lab Data Anal & Computat Coll Math & Computat Sci Guilin 541004 Peoples R China Shanghai Univ Dept Math Shanghai Peoples R China

In this paper, we consider the nonnegative tensor least squares problem, which arises in the color image restoration. Based on the BB stepsize technique, we design a nonmonotonic descent stepsize and then derive a new gradient projection algorithm to solve this problem. The convergence analysis of the new gradient projected algorithm is given. Some numerical examples show that the new method is feasible and effective. Especially, some simulation experiments in the color image restoration problems illustrate that our algorithm is more effective than the existed algorithms.

关键词： convergence analysis gradient projection algorithm nonmonotonic descent stepsize nonnegative tensor least squares problem

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UAVs to the Rescue: Prolonging the Lifetime of Wireless Devices Under Disaster Situations

IEEE TRANSACTIONS ON GREEN COMMUNICATIONS AND NETWORKING

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IEEE TRANSACTIONS ON GREEN COMMUNICATIONS AND NETWORKING 2019年第4期3卷 942-954页

作者： Shakhatreh, Hazim Khreishah, Abdallah Ji, Bo Yarmouk Univ Dept Telecommun Engn Irbid 21163 Jordan New Jersey Inst Technol Dept Elect & Comp Engn Newark NJ 07102 USA Temple Univ Dept Comp & Informat Sci Philadelphia PA 19122 USA

Unmanned aerial vehicles (UAVs) can be used as aerial wireless base stations when cellular networks go down. Prior studies on UAV-based wireless coverage typically consider downlink scenarios from an aerial base station to ground users. In this paper, we consider an uplink scenario under disaster situations (such as earthquakes or floods), when cellular networks are down. We formulate the placement problem of UAVs, where the objective is to determine the locations of a set of UAVs that maximize the time duration of uplink transmission until the first wireless device runs out of energy. We prove that this problem is NP-complete. Due to its intractability, we start by restricting the number of UAVs to be one. We show that under this special case the problem can be formulated as a convex optimization problem under a restriction on the coverage angle of the ground users. After that, we propose a gradient projection-based algorithm to find the optimal location of the UAV. Based on this, we then develop an efficient algorithm for the general case of multiple UAVs. The proposed algorithm starts by clustering the wireless devices into several clusters where each cluster being served by one UAV. After it finishes clustering the wireless devices, it applies the gradient projection-based algorithm in each cluster. We also formulate the problem of minimizing the number of UAVs required to serve the ground users such that the time duration of uplink transmission of each wireless device is greater than or equal to a threshold value. We prove that this problem is NP-complete and propose to use two efficient methods to determine the minimum number of UAVs required to serve the wireless devices. We validate the analysis by simulations and demonstrate the effectiveness of the proposed algorithms under different cases.

关键词： Unmanned aerial vehicles lifetime of wireless devices emergency response convex optimization gradient projection algorithm k-means clustering algorithm

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A constrained total variation model for single image dehazing

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PATTERN RECOGNITION 2018年 80卷 196-209页

作者： Wang, Wei He, Chuanjiang Xia, Xiang-Gen Shenzhen Univ Coll Informat Engn Shenzhen Peoples R China Chongqing Univ Coll Math & Stat Chongqing 401331 Peoples R China Univ Delaware Dept Elect & Comp Engn Newark DE 19716 USA

Haze removal (or dehazing) is very important for many applications in computer vision. Because depth information and atmospheric light are usually unknown in practice, haze removal is a challenging problem, especially for single image dehazing. In this paper, we propose a new variational model for removing haze from a single input image. The proposed model combines Koschmieder's law with Retinex assumption that an image is the product of illumination and reflection. We assume that scene depth and surface radiance are spatially piecewise smooth, total variation is thus used for regularization in our model. The proposed model is defined as a constrained optimization problem, which is solved by an alternating minimization scheme and a fast gradient projection algorithm. Theoretical analyses are given for the proposed model and algorithm. Some numerical examples are presented, which have shown that our model has the best visual effect and the highest average PSNR (Peak Signal-to-Noise Ratio) compared to six relevant models in the literature. (C) 2018 Elsevier Ltd. All rights reserved.

关键词： Dehazing Total variation Variational method gradient projection algorithm

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Optimal Placement of a UAV to Maximize the Lifetime of Wireless Devices 14

Optimal Placement of a UAV to Maximize the Lifetime of Wirel...

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14th IEEE International Wireless Communications and Mobile Computing Conference (IWCMC)

作者： Shakhatreh, Hazim Khreishah, Abdallah New Jersey Inst Technol Dept Elect & Comp Engn Newark NJ 07102 USA

ISBN: (纸本)9781538620700

关键词： Unmanned aerial vehicles lifetime of wireless network emergency response convex optimization gradient projection algorithm

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Nonlinear model predictive control of functional electrical stimulation

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CONTROL ENGINEERING PRACTICE 2017年 58卷 319-331页

作者： Kirsch, Nicholas Alibeji, Naji Sharma, Nitin Univ Pittsburgh Dept Mech Engn & Mat Sci Pittsburgh PA 15261 USA

Minimizing the amount of electrical stimulation can potentially mitigate the adverse effects of muscle fatigue during functional electrical stimulation (FES) induced limb movements. A gradient projection based model predictive controller is presented for optimal control of a knee extension elicited via FES. A control Lyapunov function was used as a terminal cost to ensure stability of the model predictive control. The controller validation results show that the algorithm can be implemented in real-time with a steady-state RMS error of less than 2 degrees. The experiments also show that the controller follows step changes in desired angles and is robust to external disturbances. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Functional electrical stimulation Nonlinear model predictive control Muscle parameter identification Rehabilitation engineering gradient projection algorithm

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Strong convexity of sandwiched entropies and related optimization problems

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REVIEWS IN MATHEMATICAL PHYSICS 2018年第9期30卷

作者： Bhatia, Rajendra Jain, Tanvi Lim, Yongdo Ashoka Univ Sonepat 131029 Haryana India Indian Stat Inst New Delhi 110016 India Sungkyunkwan Univ Dept Math Suwon 440746 South Korea

We present several theorems on strict and strong convexity, and higher order differential formulae for sandwiched quasi-relative entropy (a parametrized version of the classical fidelity). These are crucial for establishing global linear convergence of the gradient projection algorithm for optimization problems for these functions. The case of the classical fidelity is of special interest for the multimarginal optimal transport problem (the n-coupling problem) for Gaussian measures.

关键词： Positive definite matrix multimarginal optimal transport fidelity sand-wiched quasi-relative entropy strong convexity gradient projection algorithm

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Optimal Placement of a UAV to Maximize the Lifetime of Wireless Devices

Optimal Placement of a UAV to Maximize the Lifetime of Wirel...

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International Wireless Communications and Mobile Computing Conference

作者： Hazim Shakhatreh Abdallah Khreishah Department of Electrical and Computer Engineering New Jersey Institute of Technology

关键词： Unmanned aerial vehicles Lifetime of wireless network Emergency response Convex optimization gradient projection algorithm

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