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Algorithm Implementation for Distributed convex Intersection Computation

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Journal of Systems Science & Complexity 2020年第1期33卷 15-25页

作者： WANG Bingchang YU Xin PANG Dandan School of Control Science and Engineering Shandong UniversityJinan 250061China School of Information and Electrical Engineering Shandong Jianzhu UniversityJinan 250101China

Intersection computation of convex sets is a typical problem in distributed *** this paper,the algorithm implementation is investigated for distributed convex intersection computation *** a multi-agent network,each agent is associated with a convex *** objective is for all the agents to achieve an agreement within the intersection of the associated convex sets.A distributed"projected consensus algorithm"is employed,and the computation of the projection term is converted to a constrained optimization *** solution of the optimization problem is determined by Karush-Kuhn-Tucker(KKT)*** implementable algorithms based on the simplex method are introduced to solve the optimization *** numerical examples are given to illustrate the effectiveness of the algorithms.

关键词： convex intersection computation feasible direction method Lemke algorithm projected consensus algorithm

Non-convex optimization for inverse problem solving in computer-generated holography

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Light(Science & Applications) 2024年第8期13卷 1464-1486页

作者： Xiaomeng Sui Zehao He Daping Chu Liangcai Cao Department of Precision Instruments Tsinghua UniversityBeijing 100084China Department of Engineering Centre for Photonic Devices and SensorsUniversity of Cambridge9 JJ Thomson AvenueCambridge CB30FAUK Cambridge University Nanjing Centre of Technology and Innovation 23 Rongyue RoadJiangbei New AreaNanjing 210000China

Computer-generated holography is a promising technique that modulates user-defined wavefronts with digital *** appropriate holograms with faithful reconstructions is not only a problem closely related to the fundamental basis of holography but also a long-standing challenge for researchers in general fields of *** the exact solution of a desired hologram to reconstruct an accurate target object constitutes an ill-posed inverse *** general practice of single-diffraction computation for synthesizing holograms can only provide an approximate answer,which is subject to limitations in numerical *** non-convex optimization algorithms are thus designed to seek an optimal solution by introducing different constraints,frameworks,and ***,we overview the optimization algorithms applied to computer-generated holography,incorporating principles of hologram synthesis based on alternative projections and gradient descent *** is aimed to provide an underlying basis for optimized hologram generation,as well as insights into the cuttingedge developments of this rapidly evolving field for potential applications in virtual reality,augmented reality,head-up display,data encryption,laser fabrication,and metasurface design.

关键词： optimization convex inverse

A convex relaxation approach for power flow problem

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Journal of Modern Power Systems and Clean Energy 2019年第6期7卷 1399-1410页

作者： Saeed D.MANSHADI Guangyi LIU Mohammad E.KHODAYAR Jianhui WANG Renchang DAI Electrical and Computer Engineering Department San Diego State UniversitySan DiegoCA 92182USA Global Energy Interconnection Research Institute North America San JoseCA 95134USA Department of Electrical and Computer Engineering Southern Methodist UniversityDallasTX 75275USA

A solution to the power flow problem is imperative for many power system applications and several iterative approaches are employed to achieve this ***,the chance of finding a solution is dependent on the choice of the initial point because of the nonconvex feasibility region of this *** this paper,a non-iterative approach that leverages a convexified relaxed power flow problem is employed to verify the existence of a feasible *** ensure the scalability of the proposed convex relaxation,the problem is formulated as a sparse semi-definite programming *** variables associated with each maximal clique within the network form several positive semidefinite *** and network reconfiguration schemes are employed to improve the tightness of the proposed convex relaxation in order to validate the existence of a feasible solution for the original non-convex *** case studies including an ill-conditioned power flow problem are examined to show the effectiveness of the proposed approach to find a feasible solution.

关键词： convex relaxation Ill-conditioned power flow Power flow Network reconfiguration

A novel method for virtual clearance computation of high-speed train based on model integration and convex hull

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Journal of Central South University 2017年第10期24卷 2458-2467页

作者： YI Bing LI Xiong-bing ZENG Wei SONG Yong-feng YANG Yue School of Traffic and Transportation Engineering Central South UniversityChangsha 410075China

The 3D clearance of a high-speed train(HST) is critical to ensure the safety of railway transportation. Many studies have been conducted on the inspection of the clearance profile in railway operation based on the vision system, but few researchers have focused on the computation of the 3D clearance in the design phase of an HST. This paper summarizes the virtual 3D clearance computation of an HST based on model integration and the convex hull method. First, both the aerodynamic and kinetic analysis models of the HST are constructed. The two models are then integrated according to the corresponding relationship map, and an array of transformation matrixes of the HST is created to drive the designed model simulating the physical railway motion. Furthermore, the convex hull method is adopted to compute the 3D envelope of the moving train. Finally, the Hausdorff metric is involved in the measurement of the minimum clearance model and the 3D envelope model. In addition, the color map of the Hausdorff distance is established to verify that the designed shape of the HST meets the national standards. This paper provides an effective method to accurately calculate the 3D clearance for the shape design of an HST, which greatly reduces the development cost by minimizing the physical prototype that must be built.

关键词： high-speed train 3D clearance convex hull model integration Hausdorff distance

Multiple-constraint cooperative guidance based on two-stage sequential convex programming

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Chinese Journal of Aeronautics 2020年第1期33卷 296-307页

作者： Wei DONG Qiuqiu WEN Qunli XIA Shengjiang YANG School of Aerospace Engineering Beijing Institute of TechnologyBeijing 100081China Beijing Aerospace Technology Institute Beijing 100074China

An improved approach is presented in this paper to implement highly constrained cooperative guidance to attack a stationary *** problem with time-varying Proportional Navigation(PN)gain is first formulated as a nonlinear optimal control problem,which is difficult to solve due to the existence of nonlinear kinematics and nonconvex *** convexification treatments and discretization,the solution to the original problem can be approximately obtained by solving a sequence of Second-Order Cone Programming(SOCP)problems,which can be readily solved by state-of-the-art Interior-Point Methods(IPMs).To mitigate the sensibility of the algorithm on the user-provided initial profile,a Two-Stage Sequential convex Programming(TSSCP)method is presented in ***,numerical simulations under different mission scenarios are conducted to show the superiority of the proposed method in solving the cooperative guidance *** research indicated that the TSSCP method is more tractable and reliable than the traditional methods and has great potential for real-time processing and on-board implementation.

关键词： convex optimization Cooperative guidance Guidance Multiple constraints Second-order cone programming Sequential convex programming

convex mappings on some circular domains

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Science China Mathematics 2010年第5期53卷 228-237页

作者： Hong Yi Chen WenGe S China Univ Technol Dept Math Guangzhou 510640 Guangdong Peoples R China

In this paper,we consider some circular *** we give an extension theorem for some normalized biholomorphic convex mapping on some circular ***,we discover the normalized biholomorphic convex mapping on some circular d... 详细信息

关键词： circular domain biholomorphic convex mapping Minkowski functional Schwarz lemma

Effects of the convex Topography on Railway Environmental Vibrations

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Computer Modeling in Engineering & Sciences 2019年第1期118卷 177-205页

作者： Huaxi Lu Zhicheng Gao Luyao Xu Bitao Wu Department of Civil Engineering East China Jiaotong UniversityNanchang330013China.

The railway environmental vibration caused by high-speed railways is harmful to the human health,the structural safety of adjacent buildings,and the normal use of precision *** the same time,it occurs *** this case,the railway environmental vibration has drawn much attention with the rapid development of highspeed *** in Earthquake Engineering show that a convex topography has a great impact on ground vibrations,however,there is no consideration about the convex topographic effect in the study of the railway environmental vibration when the convex topography is near the *** this paper,the influence of a convex topography on the railway environmental vibration was ***-dimensional(2D)finite element models consist of subgrade-convex topography and subgrade-flat topography are established using the finite element *** length and the height of the analysis model are taken as 200 m and 41.3 m,*** external soil of the calculation model is simulated via the artificial *** comparison with measured results,the 2D finite element models were verified to be *** convex topographic effect is studied by conducting parameter investigations,such as the bottom width,cross-sectional shape,height-width ratio and the foundation soil *** show that the dimension and cross-section shape of the convex topography and the foundation soil properties have significant effect on the convex topographic effect.

关键词： Railway environmental vibration convex topography ground acceleration ground displacement frequency spectra.

Efficient predictions of formation energies and convex hulls from density functional tight binding calculations

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Journal of Materials Science & Technology 2023年第10期141卷 236-244页

作者： Anshuman Kumar Zulfikhar A.Ali Bryan M.Wong Materials Science&Engineering Program University of California-RiversideRiverside92521CAUSA Department of Physics&Astronomy University of California-RiversideRiverside92521CAUSA Materials Science&Engineering Program Department of Chemical&Environmental EngineeringDepartment of Physics&Astronomyand Department of ChemistryUniversity of California-RiversideRiverside92521CAUSA

Defects in materials significantly alter their electronic and structural properties,which affect the per-formance of electronic devices,structural alloys,and functional ***,calculating all the possible defects in complex materials with conventional Density Functional Theory(DFT)can be compu-tationally *** enhance the efficiency of these calculations,we interfaced Density Functional Tight Binding(DFTB)with the Clusters Approach to Statistical Mechanics(CASM)software package for the first *** SiC and ZnO as representative examples,we show that DFTB gives accurate results and can be used as an efficient computational approach for calculating and pre-screening formation ener-gies/convex *** DFTB+CASM implementation allows for an efficient exploration(up to an order of magnitude faster than DFT)of formation energies and convex hulls,which researchers can use to probe other complex systems.

关键词： CASM DFTB DFT Formation energy convex hull

Rigidity for convex mappings of Reinhardt domains and its applications

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Science China Mathematics 2019年第5期62卷 901-920页

作者： Taishun Liu Xiaomin Tang Jianfei Wang Department of Mathematics Huzhou University School of Mathematical Sciences Huaqiao University Department of Mathematics Zhejiang Normal University

In this paper, we investigate rigidity and its applications to extreme points of biholomorphic convex mappings on Reinhardt domains. By introducing a version of the scaling method, we precisely construct many unbounded convex mappings with only one in?nite discontinuity on the boundary of this domain. We also give a rigidity of these unbounded convex mappings via the Kobayashi metric and the Liouville-type theorem of entire functions. As an application we obtain a collection of extreme points for the class of normalized convex mappings. Our results extend both the rigidity of convex mappings and related extreme points from the unit ball to Reinhardt domains.

关键词： convex mapping Reinhardt domain scaling method Kobayashi metric extreme point