A family of the local convergence of the improved secant methods for nonlinear equality constrained optimization subject to bounds on variables

This paper studies a family of the local convergence of the improved secant methods for solving the nonlinear equality constrained optimization subject to bounds on variables. The Hessian of the Lagrangian is approximated using the DFP or the BFGS secant updates. The improved secant methods are used to generate a search direction. Combining with a suitable step size, each iterate switches to trial step of strict interior feasibility. When the Hessian is only positive definite in an affine null subspace, one shows that the algorithms generate the sequences converging q-linearly and two-step q-superlinearly. Furthermore, under some suitable assumptions, some sequences generated by the algorithms converge locally one-step q-superlinearly. Finally, some numerical results are presented to illustrate the effectiveness of the proposed algorithms.     

A line search filter secant method for nonlinear equality constrained optimization

<正> This paper formulates and analyzes a line search method for general nonlinear equalityconstrained optimization based on filter methods for step acceptance and secant methods for searchdirection.The feature of the new algorithm is that the secant algorithm is used to produce a searchdirection,a backtracking line search procedure is used to generate step size,some filtered rules areused to determine step acceptance,second order correction technique is used to reduce infeasibility andovercome the Maratos effect.Global convergence properties of this method are analyzed:under mildassumptions it is showed that every limit point of the sequence of iterates generated by the algorithmis feasible,and that there exists at least one limit point that is a stationary point for the problem.Moreover,it is also established that the Maratos effect can be overcome in our new approach by addingsecond order correction steps so that fast local superlinear convergence to a second order sufficient localsolution is achieved.Finally,the results of numerical experiments are reported to show the effectivenessof the line search filter secant method.     

A TRUST REGION ALGORITHM WITH NULL SPACE TECHNIQUE FOR EQUALITY CONSTRAINED OPTIMIZATION

This paper presents a trust region algorithm with null space technique fornonlinear equality constrained optimization. Considering in the null space methods that,the convergent rate of range space step is faster than the null space step for the most cases,the proposed algorithm computes null steps more often than range space step. Moreover,the new algorithm is based on the reduced Hessian SQP method. Global convergence ofthe proposed algorithm is proved. The effectiveness of the method is demonstrated bysome numerical examples.     

A nonmonotone line search filter method with reduced Hessian updating for nonlinear optimization

This paper proposes a nonmonotone line search filter method with reduced Hessian updating for solving nonlinear equality constrained optimization. In order to deal with large scale problems, a reduced Hessian matrix is approximated by BFGS updates. The new method assures global convergence without using a merit function. By Lagrangian function in the filter and nonmonotone scheme, the authors prove that the method can overcome Maratos effect without using second order correction step so that the locally superlinear convergence is achieved. The primary numerical experiments are reported to show effectiveness of the proposed algorithm.     

A line search filter inexact SQP method for nonlinear equality constrained optimization

This paper proposes an inexact SQP method in association with line search filter technique for solving nonlinear equality constrained optimization.For large-scale applications,it is expensive to get an exact search direction,and hence the authors use an inexact method that finds an approximate solution satisfying some appropriate conditions.The global convergence of the proposed algorithm is established by using line search filter technique.The second-order correction step is used to overcome the Maratos effect,while the line search filter inexact SQP method has q-superlinear local convergence rate.Finally,the results of numerical experiments indicate that the proposed method is efficient for the given test problems.     

An affine scaling derivative-free trust region method with interior backtracking technique for bounded-constrained nonlinear programming

This paper proposes an arlene scaling derivative-free trust region method with interior backtracking technique for bounded-constrained nonlinear programming. This method is designed to get a stationary point for such a problem with polynomial interpolation models instead of the objective function in trust region subproblem. Combined with both trust region strategy and line search technique, at each iteration, the affine scaling derivative-free trust region subproblem generates a backtracking direction in order to obtain a new accepted interior feasible step. Global convergence and fast local convergence properties are established under some reasonable conditions. Some numerical results are also given to show the effectiveness of the proposed algorithm.     

航空发动机机载模型迭代计算优化方法研究

航空发动机是一个复杂、时变的多变量热力物理系统,其部件级模型的收敛精度与收敛速度对基于模型的发动机健康管理和容错控制等领域研究具有重要意义。现有的发动机部件级模型一般基于传统拟牛顿法进行各平衡方程的联立求解,较于传统牛顿-拉夫逊法(N-R法)收敛速度得到优化,但难以满足全包线范围内动态模型机载化应用的精度兼实时性要求。提出了一种自适应变步长因子拟牛顿法,可在保证模型计算精度的同时,最大程度地减少模型迭代次数,从而大幅提升模型计算速度,为模型的机载化应用创造条件。基于现役发动机计算平台MPC5554微控制器的仿真实验结果表明：相比于传统算法,所提算法具有更好的收敛性与实时性。     

针对任意非高斯信号的快速固定点盲波束形成方法

峭度最大化盲波束形成算法的性能受步长调节参数的选择影响很大,尤其是在信道和信号参数未知的条件下,很难选择合适的步长。针对以上问题,提出了两种新的不需要步长调节参数,而且同样适用于任意非高斯信号的快速固定点的盲波束形成算法。首先通过白化对数据进行预先处理,然后以峭度最大化和波束形成器的权值正交化来构造代价函数,采用复数近似牛顿方法对代价函数优化,得到新的盲波束形成算法。与峭度最大化盲波束形成算法相比,该算法误差小、收敛速度快,不需要任何步长调节参数,更适用于信道和信号未知的环境。仿真实验验证了算法的有效性。     

求解大规模多背包问题的高级人工鱼群算法

针对复杂的大规模多背包问题,提出了一种基于高级人工鱼群算法的求解方法。为了解决人工鱼群算法收敛速度慢、求解精度低的问题,所提算法通过改进其初始化方法,优化人工鱼个体的行为选择方式和追尾行为来加快问题求解的收敛速度;同时引入了动态视野及步长和人工鱼调整策略来提高算法搜索的精度。仿真实验表明:与现有的算法相比,所提算法不仅能快速收敛,而且可以达到更高的精度,尤其是对于规模越大的多背包问题算法性能提升越明显。     

基于自适应混合能量参数的变步长LMS水声信道均衡算法

提出了一种新的变步长算法,并将该算法用于水声信道均衡。该算法克服改进归一化最小均方(developed normanized least mean square, XENLMS)算法依赖固定能量参数λ的局限性,遵循变步长算法的步长调整原则在XENLMS算法的基础上引入一个自适应混合能量参数λk,改善算法收敛速度和鲁棒性。首先通过仿真分析变步长算法中的3个固定参数α,β,μ的取值范围及对算法收敛性能的影响;并在两种典型的水声信道环境下,采用两种调制信号对算法的收敛性能进行计算机仿真,结果显示,新算法的收敛速度明显快于XENLMS算法和已有的变步长算法,收敛性能接近递归最小二乘(recursive least square, RLS) 算法的最优性能,但计算复杂度远小于RLS算法。最后,木兰湖试验验证了带判决反馈均衡器(decision feedback equalization, DFE)结构的新算法具有较好的克服多径效应和多普勒频移补偿的能力,相比LMS-DFE提高了一个数量级。     

CONVERGENCE PROPERTIES OF PROJECTED GRADIENT METHODS WITH NONMONOTONIC BACK TRACKING TECHNIQUE FOR CONVEX CONSTRAINED OPTIMIZATION

1. IntroductionGiven some function f(x): Wu - FI over a nonempty closed set n C W", one is interestedin solving the fOllowing optimization problem with constraints amin f(x)s.t. x E n (1.1)where f(x): Q C Wu - FI is twice continuously differentiable. This problem has receivedconsiderable attention extensively. The linear constrained case where n is a polyhedron is ofspecial inferest. Recently, there are quite a few articles proposing projected gradient methodsto solve the problem (see, fo…     

A new <Emphasis Type="Italic">ɛ</Emphasis>-generalized projection method of strongly sub-feasible directions for inequality constrained optimization

In this paper, the nonlinear optimization problems with inequality constraints are discussed. Combining the ideas of the strongly sub-feasible directions method and the ɛ-generalized projection technique, a new algorithm starting with an arbitrary initial iteration point for the discussed problems is presented. At each iteration, the search direction is generated by a new ɛ-generalized projection explicit formula, and the step length is yielded by a new Armijo line search. Under some necessary assumptions, not only the algorithm possesses global and strong convergence, but also the iterative points always get into the feasible set after finite iterations. Finally, some preliminary numerical results are reported.     

基于遗传算法的伺服系统摩擦参数辨识研究

LuGre摩擦模型能够精确描述摩擦环节的动态特性 ,但由于其高度非线性 ,使得参数辨识非常困难。针对LuGre摩擦模型 ,提出一种新型的基于遗传算法的模型参数两步辨识方法。首先通过Stribeck曲线 ,辨识出摩擦模型中的静态参数 ,然后由系统的稳态极限环振荡响应 ,辨识出摩擦模型的动态参数。在每一步辨识中 ,均采用遗传算法作为优化工具 ,从而避免了采用线性辩识方法时的局部极小问题。对提出的方法进行了数字仿真 ,并通过设计摩擦补偿环节 ,对辨识参数进行验证 ,结果表明了该方法的有效性。     

Blind estimation of phase offset in OFDM subcarrier for coherent demodulation

An adaptive algorithm named low complexity phase offset estimation (LC-POE) is proposed for orthogonal frequency division multiplexing (OFDM) signals. Depending on the requirement, the estimation procedure is divided into several scales to accelerate the adaptive convergence speed and ensure the estimation accuracy. The true phase offset is estimated through shrinking the detection range and raising the resolution scale step by step. Both the convergence performance and complexity are discussed in the paper. Simulation results show the effectiveness of the proposed algorithm. The LC-POE algorithm is promising in the application of OFDM systems.     

一种新的变步长LMS自适应滤波算法及性能分析

研究了自适应最小均方误差(least mean squares,LMS)滤波算法的步长选取问题。在详细分析现有变步长LMS算法的基础上,给出一种以双曲正切函数的改进形式为变步长的LMS算法。讨论了步长参数的选取原则及其对算法收敛性、抗干扰性和稳态误差的影响。该算法不但具有较快的收敛速度和跟踪速度,而且能获得更小的稳态失调。理论分析和仿真结果表明,该算法具有更好的稳态性能。     

模糊步长LMS算法及其性能分析

以均方误差、输出与误差信号的相关系数作为衡量LMS算法收敛程度的标准及模糊推理系统的输入,提出了一种用零阶Sugeno模糊推理系统自适应调整步长的模糊步长LMS(FSS-LMS)算法,并从理论上分析了FSS-LMS算法的计算复杂度及其收敛性能。分析结果指出FSS-LMS算法的计算复杂度与传统LMS算法基本相当,但它具有更大的灵活性。自适应系统辨识的仿真结果表明FSS-LMS比传统的LMS算法及其它一些变步长LMS算法具有更好的收敛性能。     

Super-resolution image reconstruction based on three-step-training neural networks

A new method of super-resolution image reconstruction is proposed, which uses a three-step-training error backpropagation neural network (BPNN) to realize the super-resolution reconstruction (SRR) of satellite image. The method is based on BPNN. First, three groups learning samples with different resolutions are obtained according to image observation model, and then vector mappings are respectively used to those three group learning samples to speed up the convergence of BPNN, at last, three times consecutive training are carried on the BPNN. Training samples used in each step are of higher resolution than those used in the previous steps, so the increasing weights store a great amount of information for SRR, and network performance and generalization ability are improved greatly. Simulation and generalization tests are carried on the well-trained three-step-training NN respectively, and the reconstruction results with higher resolution images verify the effectiveness and validity of this method.     

隐式两步混合法

本文构造了三类两步混合方法，其中一类为Ａ稳定的四阶隐式方法，一类为接近Ａ稳定的五阶隐式方法，最后一类为四阶预估－校正混合方法，其稳定区域在负实轴上超过了四级四阶Ｒｕｎｇｅ－Ｋｕｔａ方法的稳定区域，而每积分一步其右函数计算只需三次。对于这三类方法文中均作了精度阶、稳定性、收敛性等的分析，并讨论了四阶预估－校正混合方法的并行实现。     

A nonmonotone filter line search technique for the MBFGS method in unconstrained optimization

This paper presents a new nonmonotone filter line search technique in association with the MBFGS method for solving unconstrained minimization. The filter method, which is traditionally used for constrained nonlinear programming （NLP）, is extended to solve unconstrained NLP by converting the latter to an equality constrained minimization. The nonmonotone idea is employed to the filter method so that the restoration phrase, a common feature of most filter methods, is not needed. The global convergence and fast local convergence rate of the proposed algorithm are established under some reasonable conditions. The results of numerical experiments indicate that the proposed method is efficient,     

基于注意力机制的堆叠LSTM网络雷达HRRP序列目标识别方法

传统的雷达高分辨距离像(high resolution range profile, HRRP)序列识别方法依赖于人工特征提取, 并且现有的深度学习方法存在梯度消失问题, 导致收敛速度慢, 识别精度低。针对上述问题, 提出一种基于注意力机制的堆叠长短时记忆(attention-based stacked long short-term memory, Attention-SLSTM)网络模型, 该模型通过堆叠多个长短时记忆(long short-term memory, LSTM)网络层, 实现了HRRP序列更深层次抽象特征的提取; 通过替换模型的激活函数, 减缓了堆叠LSTM(stacked LSTM, SLSTM)模型梯度消失问题; 引入注意力机制计算特征序列的分配权重并用于分类识别步骤, 增强了隐藏层特征的非线性表达能力。模型在雷达目标识别标准数据集MSTAR上多种不同目的的实验结果表明, 所提方法具有更快的收敛速度和更好的识别性能, 与多种现有方法对比具有更高的识别率, 证明了所提方法的正确性和有效性。