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nonlinear optimization of the modern synchrotron radiation storage ring based on frequency map analysis

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Chinese Physics C 2009年第2期33卷 127-134页

作者：田顺强刘桂民李浩虎后接陈光玲万承兰 Shanghai Institute of Applied Physics Chinese Academy of Sciences Graduate University of Chinese Academy of Sciences

In this paper, we present a rule to improve the nonlinear solution with frequency map analysis （FMA）, and without frequently revisiting the optimization algorithm. Two aspects of FMA are emphasized. The first one is the tune shift with amplitude, which can be used to improve the solution of harmonic sextupoles, and thus obtain a large dynamic aperture. The second one is the tune diffusion rate, which can be used to select a quiet tune. Application of these ideas is carried out in the storage ring of the Shanghai Synchrotron Radiation Facility （SSRF）, and the detailed processes, as well as better solutions, are presented in this paper. Discussions about the nonlinear behaviors of off-momentum particles are also presented.

关键词： SSRF storage ring nonlinear optimization dynamic aperture FMA

Improved nonlinear optimization in the storage ring of the modern synchrotron radiation light source

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Chinese Physics C 2009年第1期33卷 65-73页

作者：田顺强刘桂民后接陈光玲陈森玉 Shanghai Institute of Applied Physics Chinese Academy of Sciences Graduate University of Chinese Academy of Sciences Institute of High Energy Physics Chinese Academy of Sciences

In the storage ring of the third generation light sources, nonlinear optimization is an indispensable course in order to obtain ample dynamic acceptances and to reach high injection efficiency and long beam lifetime, especially in a low emittance lattice. An improved optimization algorithm based on the single resonance approach, which takes relative weight and initial Harmonic Sextupole Integral Strength （HSIS） as search variables, is discussed in this paper. Applications of the improved method in several test lattices are presented. Detailed analysis of the storage ring of the Shanghai Synchrotron Radiation Facility （SSRF） is particularly emphasized. Furthermore, cancellation of the driving terms is investigated to reveal the physical mechanism of the harmonic sextupole compensation. Sensitivity to the weight and the initial HSIS as well as dependence of the optimum solution on the convergent factor is analyzed.

关键词： storage ring nonlinear optimization harmonic compensation single resonance approach

APPLICATIONS OF nonlinear optimization METHODTO NUMERICAL STUDIES OF ATMOSPHERICAND OCEANIC SCIENCES

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Applied Mathematics and Mechanics(English Edition) 2005年第5期26卷 636-646页

作者：段晚锁穆穆 LASG Institute of Atmospheric Physics Chinese Academy of Sciences Beijing 100029 P.R.China

Linear singular vector and linear singular value can only describe the evolution of sufficiently small perturbations during the period in which the tangent linear model is valid. With this in mind,the applications of nonlinear optimization methods to the atmospheric and oceanic sciences are introduced, which include nonlinear singular vector (NSV) and nonlinear singular value (NSVA), conditional nonlinear optimal perturbation (CNOP), and their applications to the studies of predictability in numerical weather and climate prediction. The results suggest that the nonlinear characteristics of the motions of atmosphere and oceans can be explored by NSV and CNOP. Also attentions are paid to the introduction of the classification of predictability problems, which are related to the maximum predictable time, the maximum prediction error, and the maximum allowing error of initial value and the parameters. All the information has the background of application to the evaluation of products of numerical weather and climate prediction. Furthermore the nonlinear optimization methods of the sensitivity analysis with numerical model are also introduced, which can give a quantitative assessment whether a numerical model is able to simulate the observations and find the initial field that yield the optimal simulation. Finally, the difficulties in the lack of ripe algorithms are also discussed, which leave future work to both computational mathematics and scientists in geophysics.

关键词： nonlinear optimization weather climate predictability sensitivity analysis

A GENERAL TWO-LEVEL SUBSPACE METHOD FOR nonlinear optimization

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Journal of Computational Mathematics 2018年第6期36卷 881-902页

作者： Cheng Chen Zaiwen Wen Yaxiang Yuan University of Chinese Academy of Sciences Beijing 100190 China LSEC ICMSEC Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China Beijing International Center for Mathematical Research Peking University Beijing 100871 China LSEC ICMSEC Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China

A new two-level subspace method is proposed for solving the general unconstrained minimization formulations discretized from infinite-dimensional optimization problems. At each iteration, the algorithm executes either a direct step on the current level or a coarse subspace correction step. In the coarse subspace correction step, we augment the traditional coarse grid space by a two-dimensional subspace spanned by the coordinate direction and the gradient direction at the current point. Global convergence is proved and convergence rate is studied under some mild conditions on the discretized functions. Preliminary numerical experiments on a few variational problems show that our two-level subspace method is promising.

关键词： nonlinear optimization Convex and nonconvex problems Subspace technique Multigrid/multilevel method Large-scale problems

A NONMONOTONE TRUST REGION ALGORITHM FOR nonlinear optimization SUBJECT TO GENERAL CONSTRAINTS

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Journal of Computational Mathematics 2003年第2期21卷 237-246页

作者： Hongchao Zhang+ (Department of Mathematics, University of Florida, Gainesville, FL, USA 32611 ) Department of Mathematics University of Florida 美国 Gainesville

In this paper we present a nonmonotone trust region algorithm for general nonlinear constrained optimization problems. The main idea of this paper is to combine Yuan's technique[1] with a nonmonotone method similar to Ke and Han [2]. This new algorithm may not only keep the robust properties of the algorithm given by Yuan, but also have some advantages led by the nonmonotone technique. Under very mild conditions, global convergence for the algorithm is given. Numerical experiments demonstrate the efficiency of the algorithm.

关键词： nonlinear optimization Nonmonotone algorithm Trust region General con-straintss

GLOBAL CONVERGENCE OF TRUST REGION ALGORITHM FOR EQUALITY AND BOUND CONSTRAINED nonlinear optimization

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Applied Mathematics(A Journal of Chinese Universities) 2003年第1期18卷 83-94页

作者： TongXiaojiao ZhouShuzi Dept.ofMath. ChangshaUniv.ofElectricPowerChangsha410077China. Dept.ofMath. HunanUniv.Changsha410082China

This paper presents a trust region two phase model algorithm for solving the equality and bound constrained nonlinear optimization problem. A concept of substationary point is given. Under suitable assumptions,the global convergence of this algorithm is proved without assuming the linear independence of the gradient of active constraints. A numerical example is also presented.

关键词： nonlinear optimization equality and bound constrained problem trust-region method global convergence.

Application of nonlinear optimization method to sensitivity analysis of numerical model

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Progress in Natural Science:Materials International 2004年第6期 84-87页

作者： XU Hui 1,MU Mu 1 * and LUO Dehai 2(1. LASG,Institute of Atmospheric Physics,Chinese Academy of Sciences,Beijing 100029,China 2. Department of Atmosphere Sciences,Ocean University of China,Qingdao 266003,China) LASG Institute of Atmospheric Physics Chinese Academy of Sciences Beijing 100029 China Department of Atmosphere Sciences Ocean University of China Qingdao 266003 China

A nonlinear optimization method is applied to sensitivity analysis of a numerical model. Theoretical analysis and numerical experiments indicate that this method can give not only a quantitative assessment whether the numerical model is able to simulate the observations or not,but also the initial field that yields the optimal simulation. In particular,when the simulation results are apparently satisfactory,and sometimes both model error and initial error are considerably large,the nonlinear optimization method,under some conditions,can identify the error that plays a dominant role.

关键词： sensitivity analysis nonlinear optimization adjoint method numerical model.

SOLVING nonlinear optimization PROBLEMS BASED ON GENERALIZED CHOQUET INTEGRALS BY USING SOFT COMPUTING TECHNIQUES

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SOLVING NONLINEAR OPTIMIZATION PROBLEMS BASED ON GENERALIZED...

Visual-Inertial Odometry Design Based on nonlinear optimization and Its Online Initialization Method for the Autonomous Navigation

第11届国际模糊系统协会世界大会

作者： Marie Spilde Department of Mathematics University of Nebraska at OmahaOmahaNE 68182USA

＜正＞ The traditional gradient search fails in optimization problems where the objective function is not differentiable, such as nonlinear multiregressions based on the generalized Choquet integral with respect to signed fuzzy measures. The gradient search can be replaced with an iterative search algorithm where differences instead of differentials are applied.

关键词： Fuzzy measures Choquet integrals multiregressions nonlinear optimization soft computing.

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Visual-Inertial Odometry Design Based on Nonlinear Optimizat...