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Maneuvering Angle Rigid Formations With global convergence Guarantees

IEEE/CAA Journal of Automatica Sinica 2022年第8期9卷 1464-1475页

作者： Liangming Chen Zhiyun Lin Hector Garcia de Marina Zhiyong Sun Mir Feroskhan School of Mechanical and Aerospace Engineering Nanyang Technological UniversitySingapore 639798Singapore Department of Computer Architecture and Technology and also with CITICUniversity of Granada18014 GranadaSpain Department of Electrical Engineering Eindhoven University of Technology5600 MB Eindhoventhe Netherlands

Angle rigid multi-agent formations can simultaneously undergo translational,rotational,and scaling maneuvering,therefore combining the maneuvering capabilities of both distance and bearing rigid ***,maneuvering angle rigid formations in 2D or 3D with global convergence guarantees is shown to be a challenging problem in the existing literature even when relative position measurements are *** by angle-induced linear equations in 2D triangles and 3D tetrahedra,this paper aims to solve this challenging problem in both 2D and3D under a leader-follower *** the 2D case where the leaders have constant velocities,by using local relative position and velocity measurements,a formation maneuvering law is designed for the followers governed by double-integrator *** the leaders have time-varying velocities,a sliding mode formation maneuvering law is proposed by using the same *** the 3D case,to establish an angle-induced linear equation for each tetrahedron,we assume that all the followers'coordinate frames share a common Z ***,a formation maneuvering law is proposed for the followers to globally maneuver Z-weakly angle rigid formations in *** extension to Lagrangian agent dynamics and the construction of the desired rigid formations by using the minimum number of angle constraints are also *** examples are provided to validate the effectiveness of the proposed algorithms.

关键词： Index Terms—Angle rigid formations formation control formation maneuvering global convergence multi-agent systems

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global convergence OF A TRUST REGION ALGORITHM USING INEXACT GRADIENT FOR EQUALITY-CONSTRAINED OPTIMIZATION

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Acta Mathematica Scientia 2000年第3期20卷 365-373页

作者：童小娇周叔子 Department of Mathematics Hunan University Changsha 410082 China

A trust-region algorithm is presented for a nonlinear optimization problem of equality-constraints. The characterization of the algorithm is using inexact gradient information. global convergence results are demonstra... 详细信息

关键词： equality constraints trust region method inexact gradient global convergence

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global convergence of a Modified Limited Memory BFGS Method for Non-convex Minimization

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Acta Mathematicae Applicatae Sinica 2013年第3期29卷 555-566页

作者： Yun-hai XIAO Ting-feng Zeng-xin WEI Department of Mathematics Nanjing University Zhengzhou Technical College College of Mathematics and Information Science Guangxi University

In this paper, a modified limited memory BFGS method for solving large-scale unconstrained optimization problems is proposed. A remarkable feature of the proposed method is that it possesses global convergence property without convexity assumption on the objective function. Under some suitable conditions, the global convergence of the proposed method is proved. Some numerical results are reported which illustrate that the proposed method is efficient.

关键词： Non-convex minimization secant equation limited memory BFGS method global convergence

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global convergence of the Broyden's Class of Quasi-Newton Methods with Nonmonotone Linesearch

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Acta Mathematicae Applicatae Sinica 2003年第1期19卷 19-24页

作者： Da-chuan XuInstitute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, China Institute of Applied Mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing China

Abstract In this paper, the Broyden class of quasi-Newton methods for unconstrained optimization is investigated. Non-monotone linesearch procedure is introduced, which is combined with the Broyden's class. Under the ... 详细信息

关键词： Keywords Quasi-Newton method Broyden class non-monotone linesearch global convergence unconstrained optimization

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global convergence OF QPFTH METHOD FOR LARGE-SCALE NONLINEAR SPARSE CONSTRAINED OPTIMIZATION

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Acta Mathematicae Applicatae Sinica 1998年第3期14卷 271-283页

作者：倪勤 College of Science Nanjing University of Aeronautics and Astronautics Nanjing China

A QP-free, truncated hybrid (QPFTH) method was proposed and developed in [6] forsolving sparse large-scale nonlinear programming problems. In the hybrid method, a truncatedNewton method is combined with the method of multiplier. In every iteration level, either atruncated solution for a symmetric system of linear equations is determined by CG algorithmor an unconstrained subproblem is solved by the limited memory BFGS algorithm such thatthe hybrid algorithm is suitable to large-scale problems. In this paper, the consistency in thehybrid method and a steplength procedure are discussed and developed. The global convergenceof QPFTH method is proved and the two-step Q-quadratic convergence rate is further analyzed.

关键词： Largesscale optimization global convergence sparse problem

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global convergence of a Modified Spectral CD Conjugate Gradient Method

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Journal of Mathematical Research and Exposition 2011年第2期31卷 261-268页

作者： Wei CAO Kai Rong WANG Yi Li WANG College of Mathematics and Statistics Chongqing University Chongqing 401331 P. R. China

In this paper,we present a new nonlinear modified spectral CD conjugate gradient method for solving large scale unconstrained optimization *** direction generated by the method is a descent direction for the objective function,and this property depends neither on the line search rule,nor on the convexity of the objective ***,the modified method reduces to the standard CD method if line search is *** some mild conditions,we prove that the modified method with line search is globally convergent even if the objective function is *** numerical results show that the proposed method is very promising.

关键词： unconstrained optimization conjugate gradient method armijo-type line search global convergence

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global convergence Property of Conjugate Gradient Methods for Optimization

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Systems Science and Systems Engineering 1999年第3期9卷 277-282页

作者： LIAN Shu\|jun Institute of Operations Research, Qufu Normal University, Qufu 273165, China

In this paper, we give a new line search. With the line search, we prove the global convergence of the Hestenes\|Stiefel method.

关键词： conjugate gradient method global convergence

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global convergence of Conjugate Gradient Methods without Line Search

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Journal of Mathematical Research with Applications 2018年第5期38卷 541-550页

作者： Cuiling CHEN Yu CHEN College of Mathematics and Statistics Guangxi Normal University School of Computing and Information University of Pittsburgh

In this paper, a new steplength formula is proposed for unconstrained optimization,which can determine the step-size only by one step and avoids the line search step. global convergence of the five well-known conjugate gradient methods with this formula is analyzed,and the corresponding results are as follows:（1） The DY method globally converges for a strongly convex LC;objective function;（2） The CD method, the FR method, the PRP method and the LS method globally converge for a general, not necessarily convex, LC;objective function.

关键词： unconstrained optimization conjugate gradient method line search global convergence

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The global convergence of Self-Scaling BFGS Algorithm with Nonmonotone Line Search for Unconstrained Nonconvex Optimization Problems

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Acta Mathematica Sinica,English Series 2007年第7期23卷 1233-1240页

作者： Hong Xia YIN Dong Lei DU Chinese Academy of Sciences Research Center on Data Technology and Knowledge Economy Department of Mathematics Graduate University of the Chinese Academy of Sciences Faculty of Administration University of New Brunswick

The self-scaling quasi-Newton method solves an unconstrained optimization problem by scaling the Hessian approximation matrix before it is updated at each iteration to avoid the possible large eigenvalues in the Hessian approximation matrices of the objective function. It has been proved in the literature that this method has the global and superlinear convergence when the objective function is convex （or even uniformly convex）. We propose to solve unconstrained nonconvex optimization problems by a self-scaling BFGS algorithm with nonmonotone linear search. Nonmonotone line search has been recognized in numerical practices as a competitive approach for solving large-scale nonlinear problems. We consider two different nonmonotone line search forms and study the global convergence of these nonmonotone self-scale BFGS algorithms. We prove that, under some weaker condition than that in the literature, both forms of the self-scaling BFGS algorithm are globally convergent for unconstrained nonconvex optimization problems.

关键词： nonmonotone line search self-scaling BFGS method global convergence

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On the global convergence of a Projective Trust Region Algorithm for Nonlinear Equality Constrained Optimization

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Acta Mathematica Sinica,English Series 2018年第12期34卷 1804-1828页

作者： Yong Gang PEI De Tong ZHU Mathematics and Information Science He 'nan Normal University Xinxiang 453007 P. R. China Mathematics and Science College Shanghai Normal University Shanghai 200234 P. R. China

A trust-region sequential quadratic programming （SQP） method is developed and analyzed for the solution of smooth equality constrained optimization problems. The trust-region SQP algorithm is based on filter line search technique and a composite-step approach, which decomposes the overall step as sum of a vertical step and a horizontal step. The algorithm includes critical modifications of horizontal step computation. One orthogonal projective matrix of the Jacobian of constraint functions is employed in trust-region subproblems. The orthogonal projection gives the null space of the trans- position of the Jacobian of the constraint function. Theoretical analysis shows that the new algorithm retains the global convergence to the first-order critical points under rather general conditions. The preliminary numerical results are reported.

关键词： Sequential quadratic programming trust-region filter line search projection global convergence

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