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GLOBAL CONVERGENCE OF UNCONSTRAINED MINIMIZATION METHODS WITH A GENERALIZED backtracking LINESEARCH PROCEDURE

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Systems Science and Mathematical Sciences 1995年第2期8卷 122-127页

作者： LIU Guanghui HAN Jiye(Institute of Applied Mathematics, Academia Sinica, Beijing 100080,China) Institute of Applied Mathematics Academia Sinica Beijing 100080 China

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关键词： backtracking linesearch direction selection rule BFGS method global convergencet unconstrained optimization

Kinematic-mapping-model-guided analysis and optimization of 2-PSS&1-RR circular-rail parallel mechanism for fully steerable phased array antennas

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Defence Technology 2024年第8期38卷 136-154页

作者： Guodong Tan Xiangfei Meng Xuechao Duan Lulu Cheng Dingchao Niu Shuai He Dan Zhang Laboratory of Electromechanical Coupling in Electronic Equipment Xidian University Department of Mechanical Engineering The Hong Kong Polytechnic University

This paper presents a systematic methodology for analyzing and optimizing an innovative antenna mount designed for phased array antennas, implemented through a novel 2-PSS&1-RR circular-rail parallel mechanism. Initially, a comparative motion analysis between the 3D model of the mount and its full-scale prototype is conducted to validate effectiveness. Given the inherent complexity, a kinematic mapping model is established between the mount and the crank-slider linkage, providing a guiding framework for subsequent analysis and optimization. Guided by this model, feasible inverse and forward solutions are derived, enabling precise identification of stiffness singularities. The concept of singularity distance is thus introduced to reflect the structural stiffness of the mount. Subsequently, also guided by the mapping model, a heuristic algorithm incorporating two backtracking procedures is developed to reduce the mount's mass. Additionally, a parametric finite-element model is employed to explore the relation between singularity distance and structural stiffness. The results indicate a significant reduction(about 16%) in the antenna mount's mass through the developed algorithm, while highlighting the singularity distance as an effective stiffness indicator for this type of antenna mount.

关键词： backtracking Circular rail Crank-slider linkage Innovative antenna mount Kinematic mapping model Stiffness singularity

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非线性约束优化的既约两块校正回代算法

高等学校计算数学学报 2005年第S1期 329-335页

作者：顾益明朱德通上海师范大学数学系上海师范大学数学系上海 200234

1 引言本文考虑非线性等式约束优化问题其中f:Rn→R是连续可微函数,c(x):Rn→Rm(m≤n)为非线性实值函数．记g(x)表示目标函数f(x)的梯度▽f(x)∈Rn,用A(x)表示约束函数的雅可比矩阵,即A(x)=▽c(x):[▽c1(x),…,▽cm(x)]∈Rn×m．定义拉... 详细信息

1 引言本文考虑非线性等式约束优化问题其中f:Rn→R是连续可微函数,c(x):Rn→Rm(m≤n)为非线性实值函数．记g(x)表示目标函数f(x)的梯度▽f(x)∈Rn,用A(x)表示约束函数的雅可比矩阵,即A(x)=▽c(x):[▽c1(x),…,▽cm(x)]∈Rn×m．定义拉格朗日函数l(x,λ)=

关键词： trust region backtracking reduced.

Solving quantified constraint satisfaction problems with value selection rules

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Frontiers of Computer Science 2020年第5期14卷 153-163页

作者： Jian Gao Jinyan Wang Kuixian Wu Rong Chen College of Information Science and Technology Dalian Maritime UniversityDalian116026China Logistics Research Institute Dalian Maritime UniversityDalian116026China College of Computer Science and Information Engineering Guangxi Normal UniversityGuilin541004China

Solving a quantified constraint satisfaction problem(QCSP)is usually a hard task due to its computational *** algorithms play an important role in solving this problem,among which backtrack algorithms are *** a backtrack algorithm,an important step is assigning a variable by a chosen value when exploiting a branch,and thus a good value selection rule may speed up *** this paper,we propose two value selection rules for existentially and universally quantified variables,respectively,to avoid unnecessary *** rule for universally quantified variables is prior to trying failure values in previous branches,and the rule for existentially quantified variables selects the promising values *** rules are integrated into the state-of-the-art QCSP solver,i.e.,QCSP-Solve,which is an exact solver based on *** perform a number of experiments to evaluate improvements brought by our *** computational results,we can conclude that the new value selection rules speed up the solver by 5 times on average and 30 times at *** also show both rules perform well particularly on instances with existentially and universally quantified variables occurring alternatively.

关键词： quantified CSP backtracking value selection fail-first principle

Superlinearly Convergent Affine Scaling Interior Trust-Region Method for Linear Constrained LC^1 Minimization

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Acta Mathematica Sinica,English Series 2008年第12期24卷 2081-2100页

作者： De Tong ZHU Business College Shanghai Normal University Shanghai 200234 P. R. China

We extend the classical affine scaling interior trust region algorithm for the linear constrained smooth minimization problem to the nonsmooth case where the gradient of objective function is only locally Lipschitzian. We propose and analyze a new affine scaling trust-region method in association with nonmonotonic interior backtracking line search technique for solving the linear constrained LC1 optimization where the second-order derivative of the objective function is explicitly required to be locally Lipschitzian. The general trust region subproblem in the proposed algorithm is defined by minimizing an augmented affine scaling quadratic model which requires both first and second order information of the objective function subject only to an affine scaling ellipsoidal constraint in a null subspace of the augmented equality constraints. The global convergence and fast local convergence rate of the proposed algorithm are established under some reasonable conditions where twice smoothness of the objective function is not required. Applications of the algorithm to some nonsmooth optimization problems are discussed.

关键词： trust region method backtracking nonmonotonic technique interior point LC^1 minimization affine scaling

A heuristic method for solving triangle packing problem

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2005年第6期6卷 565-570页

作者：陈传波何大华 College of Computer Science & Technology Huazhong University of Science & Technology Wuhan 430074 China

Given a set of triangles and a rectangle container, the triangle packing problem is to determine if these triangles can be placed into the container without overlapping. Triangle packing problem is a special case of polygon packing problem and also NP-hard, so it is unlikely that an efficient and exact algorithm can be developed to solve this problem. In this paper, a new concept of rigid placement is proposed, based on which a discrete solution space called rigid solution space is constructed. Each solution in the rigid solution space can be built by continuously applying legal rigid placements one by one until all the triangles are placed into the rectangle container without overlapping. The proposed Least-Destruction-First (LDF) strategy determines which rigid placement has the privilege to go into the rectangle container. Based on this, a heuristic algorithm is proposed to solve the problem. Combining Least-Destruction-First strategy with backtracking, the corresponding backtracking algorithm is proposed. Computa- tional results show that our proposed algorithms are efficient and robust. With slight modification, these techniques can be con- veniently used for solving polygon packing problem.

关键词： Triangle packing problem Rigid placement Flexibility Destruction Least-Destruction-First (LDF) strategy backtracking

Research on Guaranteed Scheduling Algorithms

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Transactions of Tianjin University 2002年第1期8卷 48-51页

作者：张凤芝张红线宗润宽任长明天津大学电子信息工程学院天津300072 天津大学化工学院天津300072

Guaranteed scheduling is necessary for hard real time systems, because each process of them must meet their deadline, or a serious consequence will *** this paper we discuss two guaranteed schedule algorithms:backtracking and branch and bound,introduce the process to find the optimal solution by both methods,propose the concept of logical node and physical *** some experiments for different process sets,we have made comparisons between the two algorithms in branch nodes,comparing time,topology of the search tree,memory size needed,etc.

关键词： hard real time systems branch and bound backtracking guaranteed scheduling

Improved CoSaMP Reconstruction Algorithm Based on Residual Update

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Journal of Computer and Communications 2019年第6期7卷 6-14页

作者： Dongxue Lu Guiling Sun Zhouzhou Li Shijie Wang College of Electronic Information and Optical Engineering Nankai University Tianjin China

A large number of sparse signal reconstruction algorithms have been continuously proposed, but almost all greedy algorithms add a fixed number of indices to the support set in each iteration. Although the mechanism of selecting the fixed number of indexes improves the reconstruction efficiency, it also brings the problem of low index selection accuracy. Based on the full study of the theory of compressed sensing, we propose a dynamic indexes selection strategy based on residual update to improve the performance of the compressed sampling matching pursuit algorithm (CoSaMP). As an extension of CoSaMP algorithm, the proposed algorithm adopts a residual comparison strategy to improve the accuracy of backtracking selected indexes. This backtracking strategy can efficiently select backtracking indexes. And without increasing the computational complexity, the proposed improvement algorithm has a higher exact reconstruction rate and peak signal to noise ratio (PSNR). Simulation results demonstrate the proposed algorithm significantly outperforms the CoSaMP for image recovery and one-dimensional signal.

关键词： Compressed Sensing Residual Descent Reconstruction Algorithm backtracking

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中太平洋海山群漂移史及其来源

海洋地质与第四纪地质 2005年第3期25卷 35-42页

作者：赵俐红高金耀金翔龙章家保中国科学院海洋研究所国家海洋局第二海洋研究所海底科学重点实验室杭州310012

中太平洋海山群的海山呈簇状排列且近EW向展布于太平洋海山密集区,其四周分布着一系列NW走向的线性列岛及规模巨大的水下海山链.它位于明显属于海山链构造的夏威夷群岛和马绍尔群岛之间,处于莱恩群岛的北西向延伸方向上,与热点作用的板... 详细信息

中太平洋海山群的海山呈簇状排列且近EW向展布于太平洋海山密集区,其四周分布着一系列NW走向的线性列岛及规模巨大的水下海山链.它位于明显属于海山链构造的夏威夷群岛和马绍尔群岛之间,处于莱恩群岛的北西向延伸方向上,与热点作用的板内火山作用关系密切.结合前人对中太平洋海山群形成和漂移的认识,从板决运动和几何学角度出发,采用backtracking和Hot-spotting海山追踪方法对该区海山进行了追踪,发现该区海山的热点源主要位于现今法属玻利尼西亚群岛区(法属玻利尼西亚热点群),这与前人从古地磁和钻探资料出发得到的结果相接近.研究表明,中太平洋海山群是多热点成因的板内火山作用和板块构造运动的共同产物,它在130～90 Ma期间起源于法属玻利尼西亚热点群,曾随着太平洋板块发生过向南和向北的运动,既有水平方向的漂移又有垂直方向上的升降,在漂移和升降过程中还受到了当时大规模多期的热点活动和断裂活动的改造作用,经过一个漫长的过程后才到达今天的位置,最后形成了现今呈簇状分布的海山群.

关键词：中太平洋海山群 backtracking Hot-spotting 法属玻利尼西亚热点群