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A non-convex optimization Approach to Dynamic Coverage Problem of Multi-agent Systems in an Environment with Obstacles

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Journal of Systems Science & Complexity 2020年第2期33卷 426-445页

作者： MA Longbiao HE Fenghua WANG Long LI Changxi YAO Yu Control and Simulation Center Harbin Institute of TechnologyHarbin 150080China

In this paper,a cooperative region reconnaissance problem is investigated where a group of agents are required to fly across and detect events occur in an environment with static obstacles until an effective coverage is ***,the region reconnaissance is formulated as a non-convex optimization problem.A coverage performance index with additional collision and obstacle avoidance constraints is *** the optimization index is an implicit function of state variables and cannot be used to compute gradients on state variables directly,an approximate optimization index is ***,a non-convex optimization-based coverage algorithm is proposed to find the optimal reconnaissance location for each agent and guarantee no collisions trajectories among agents and ***,simulation experiments are performed to verify the effectiveness of the proposed approach.

关键词： Dynamic coverage multi-agent systems non-convex optimization obstacles region reconnaissance

An Efficient Smoothing and Thresholding Image Segmentation Framework with Weighted Anisotropic-lsotropicTotalVariation

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Communications on Applied Mathematics and Computation 2024年第2期6卷 1369-1405页

作者： Kevin Bui Yifei Lou Fredrick Park Jack Xin Department of Mathematics University of CaliforniaIrvineIrvineCA 92697-3875USA Department of Mathematics University of North CarolinaChapel HillChapel HillNC 27599.USA Department of Mathematics and Computer Science Whittier CollegeWhittierCA 90602USA

In this paper,we design an efficient,multi-stage image segmentation framework that incorporates a weighted difference of anisotropic and isotropic total variation(AITV).The segmentation framework generally consists of two stages:smoothing and thresholding,thus referred to as smoothing-and-thresholding(SaT).In the first stage,a smoothed image is obtained by an AITV-regularized Mumford-Shah(MS)model,which can be solved efficiently by the alternating direction method of multipliers(ADMMs)with a closed-form solution of a proximal operator of the l_(1)-αl_(2) *** convergence of the ADMM algorithm is *** the second stage,we threshold the smoothed image by K-means clustering to obtain the final segmentation *** experiments demonstrate that the proposed segmentation framework is versatile for both grayscale and color images,effcient in producing high-quality segmentation results within a few seconds,and robust to input images that are corrupted with noise,blur,or *** compare the AITV method with its original convex TV and nonconvex TVP(O

关键词： Image segmentation non-convex optimization Mumford-Shah(MS)model Alternating direction method of multipliers(ADMMs) Proximal operator

optimization for Deep Learning:An Overview

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Journal of the Operations Research Society of China 2020年第2期8卷 249-294页

作者： Ruo-Yu Sun Department of Industrial and Enterprise Systems Engineering and affiliated to Coordinated Science LaboratoryUniversity of Illinois at Urbana-ChampaignUrbanaIL 61801USA Department of Electrical and Computer Engineering University of Illinois at Urbana-ChampaignUrbanaIL 61801USA

optimization is a critical component in deep *** think optimization for neural networks is an interesting topic for theoretical research due to various ***,its tractability despite non-convexity is an intriguing question and may greatly expand our understanding of tractable ***,classical optimization theory is far from enough to explain many ***,we would like to understand the challenges and opportunities from a theoretical perspective and review the existing research in this ***,we discuss the issue of gradient explosion/vanishing and the more general issue of undesirable spectrum and then discuss practical solutions including careful initialization,normalization methods and skip ***,we review generic optimization methods used in training neural networks,such as stochastic gradient descent and adaptive gradient methods,and existing theoretical ***,we review existing research on the global issues of neural network training,including results on global landscape,mode connectivity,lottery ticket hypothesis and neural tangent kernel.

关键词： Deep learning non-convex optimization Neural networks Convergence Landscape

SOLVING SYSTEMS OF QUADRATIC EQUATIONS VIA EXPONENTIAL-TYPE GRADIENT DESCENT ALGORITHM

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Journal of Computational Mathematics 2020年第4期38卷 638-660页

作者： Meng Huang Zhiqiang Xu LSEC Inst.Comp.Math.Academy of Mathematics and System ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China

We consider the rank minimization problem from quadratic measurements,i.e.,recovering a rank r matrix X 2 Rn×r from m scalar measurements yi=ai XX⊤ai,ai 2 Rn,i=1,...,*** problem arises in a variety of applications such as quadratic regression and quantum state *** present a novel algorithm,which is termed exponential-type gradient descent algorithm,to minimize a non-convex objective function f(U)=14m Pm i=1(yi−a⊤i UU⊤ai)*** algorithm starts with a careful initialization,and then refines this initial guess by iteratively applying exponential-type gradient ***,we can obtain a good initial guess of X as long as the number of Gaussian random measurements is O(nr),and our iteration algorithm can converge linearly to the true X(up to an orthogonal matrix)with m=O(nr log(cr))Gaussian random measurements。

关键词： Low-rank matrix recovery non-convex optimization Phase retrieval

Robust trajectory planning for UAV communication systems in the presence of jammers

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Chinese Journal of Aeronautics 2022年第10期35卷 265-274页

作者： Lingyun ZHOU Xiaotong ZHAO Xin GUAN Enbin SONG XIN ZENG Qingjiang SHI School of Software Engineering Tongji UniversityShanghai 200092China College of Mathematics and School of Aeronautics and Astronautics Sichuan UniversityChengdu 610064China Department of Information and Communication Engineering Tongji UniversityShanghai 200092China

Unmanned Aerial Vehicle(UAV)has emerged as a promising novel application for the Sixth-Generation(6G)wireless communication by leveraging more favorable Line-of-Sight(Lo S)***,the jamming resistance by exploiting UAV’s mobility is a new challenge in the UAV-ground *** paper investigates the trajectory planning problem in an UAV communication system,where the UAV is operated by a Ground Control Unit(GCU)to perform certain tasks in the presence of multiple jammers with imperfect power and location *** ensure the reliability of the GCU-to-UAV link,we formulate the problem as a non-convex semi-infinite optimization,aiming to maximize the average worst-case Signal-toInterference-plus-Noise Ratio(SINR)over a given flight duration by designing the robust trajectory of the UAV under stringent energy availability *** handle this problem efficiently,we develop an iterative algorithm for the solution with the aid of S-procedure and Successive convex Approximation(SCA)*** results demonstrate the efficacy of our proposed algorithm and offer some useful design insights to practical system.

关键词： 6G UAV communications Jamming resistance Trajectory optimization Robust design non-convex optimization

A Positioning Method and Realization on Single Satellites in Different Orbits Using TDOA

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China Communications 2023年第7期20卷 108-121页

作者： Laiding Zhao Xun Zhu Gengxin Zhang Zhaowen Wang College of Telecommunications and Information Engineering Nanjing University of Posts and TelecommunicationsNanjing 210003China Key Laboratory of Broadband Wireless Communication and Sensor Network Technology Nanjing University of Posts and TelecommunicationsNanjing 210003China “Telecommunication and Network”National Engineering Research Center Nanjing University of Posts and TelecommunicationsNanjing 210003China Shanghai Aerospace Electronic Technology Institute Shanghai 201109China

The main geolocation technology currently used in COSPAS-SARSAT system is TDOA/FDOA or three-star TDOA,the principle is to determine the location of the signal source by using the difference in arrival time and frequency of the wireless signal between different ***,ground monitoring stations need to be equipped with more than two antenna receiving stations,and multiple satellites should be able to simultaneously relay the distress signal from the target source in order to achieve the geolocation ***,when the ground receiving system has only one antenna receiving station,or the target source is in a heavily obscured environment,the ground side is unable to receive the forwarded signals from multiple satellites at the same time,which will make it impossible to *** address these problems,in this paper,a time-sharing single satellite geolocations method based on different orbits is proposed for the first *** method uses one or several low-earth orbit satellites(LEO)and mediumearth orbit satellites(MEO)in the visible area,and the receiving station only needs one pair of receiving antennas to complete the *** can effectively compensate for the shortcomings of the traditional TDOA using the same moment and have better positioning accuracy compared with the single satellite in the same *** to the limited experimental conditions,this paper tests the navigation satellite using different orbit time-sharing single satellite geolocations,and proves that the positioning method has high positioning accuracy and has certain promotion and application value.

关键词： different orbit time-sharing non-convex optimization single satellite TDOA

FAST ALGORITHMS FOR HIGHER-ORDER SINGULAR VALUE DECOMPOSITION FROM INCOMPLETE DATA

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Journal of Computational Mathematics 2017年第4期35卷 397-422页

作者： Yangyang Xu Department of Mathematics University of Alabama Tuscaloosa AL 35487 USA

Higher-order singular value decomposition （HOSVD） is an efficient way for data reduction and also eliciting intrinsic structure of multi-dimensional array data. It has been used in many applications, and some of them involve incomplete data. To obtain HOSVD of the data with missing values, one can first impute the missing entries through a certain tensor completion method and then perform HOSVD to the reconstructed data. However, the two-step procedure can be inefficient and does not make reliable decomposition. In this paper, we formulate an incomplete HOSVD problem and combine the two steps into solving a single optimization problem, which simultaneously achieves imputation of missing values and also tensor decomposition. We also present one algorithm for solving the problem based on block coordinate update （BCU）. Global convergence of the algorithm is shown under mild assumptions and implies that of the popular higher-order orthogonality iteration （HOOI） method, and thus we, for the first time, give global convergence of HOOI. In addition, we compare the proposed method to state-of-the-art ones for solving incom- plete HOSVD and also low-rank tensor completion problems and demonstrate the superior performance of our method over other compared ones. Furthermore, we apply it to face recognition and MRI image reconstruction to show its practical performance.

关键词： multilinear data analysis higher-order singular value decomposition (HOSVD),low-rank tensor completion non-convex optimization higher-order orthogonality iteration(HOOI) global convergence.

Reserve Constrained Dynamic Economic Dispatch with Valve-point Effect:A Two-stage Mixed Integer Linear Programming Approach

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CSEE Journal of Power and Energy Systems 2017年第2期3卷 203-211页

作者： Zhaolong Wu Jianying Ding Q.H.Wu Zhaoxia Jing Jiehui Zheng School of Electric Power Engineering South China University of TechnologyGuangzhou 510641China Power Generation Commercial Division Guangdong Yudean Group Co.LTDGuangzhou 510630China

This paper proposes a deterministic two-stage mixed integer linear programming(TSMILP)approach to solve the reserve constrained dynamic economic dispatch(DED)problem considering valve-point effect(VPE).In stage one,the nonsmooth cost function and the transmission loss are piecewise linearized and consequently the DED problem is formulated as a mixed integer linear programming(MILP)problem,which can be solved by commercial *** stage two,based on the solution obtained in stage one,a range compression technique is proposed to make a further exploitation in the subspace of the whole solution *** to the linear approximation of the transmission loss,the solution obtained in stage two dose not strictly satisfies the power balance ***,a forward procedure is employed to eliminate the *** simulation results on four test systems show that TSMILP makes satisfactory performances,in comparison with the existing methods.

关键词： Dynamic economic dispatch mixed integer linear programming valve-point effect spinning reserve transmission loss non-convex optimization

Double Transformed Tubal Nuclear Norm Minimization for Tensor Completion

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Transactions of Nanjing University of Aeronautics and Astronautics 2022年第S1期39卷 166-174页

作者： TIAN Jialue ZHU Yulian LIU Jiahui College of Computer Science and Technology/College of Artificial Intelligence Nanjing University of Aeronautics and AstronauticsNanjing 211106P.R.China Fundamental Experimental Teaching Department Nanjing University of Aeronautics and Astronautics

non-convex methods play a critical role in low-rank tensor completion for their approximation to tensor rank is tighter than that of convex *** they usually cost much more time for calculating singular values of large *** this paper,we propose a double transformed tubal nuclear norm(DTTNN)to replace the rank norm penalty in low rank tensor completion(LRTC)*** turns the original non-convex penalty of a large tensor into two convex penalties of much smaller tensors,and it is shown to be an equivalent ***,DTTNN could take advantage of non-convex envelopes while saving *** results on color image and video inpainting tasks verify the effectiveness of DTTNN compared with state-of-the-art methods.

关键词： double transformed tubal nuclear norm low tubal-rank non-convex optimization tensor factorization tensor completion