A filter secant method with nonmonotone line search for equality constrained optimization

<正> This paper proposes a filter secant method with nonmonotone line search for non-linearequality constrained optimization.The Hessian of the Lagrangian is approximated using the BFGSsecant update.This new method has more flexibility for the acceptance of the trial step and requires lesscomputational costs compared with the monotone one.The global and local convergence of the proposedmethod are given under some reasonable conditions.Further,two-step Q-superlinear convergence rateis established by introducing second order correction step.The numerical experiments are reported toshow the effectiveness of the proposed algorithm.     

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,     

NONMONOTONIC TRUST REGION PROJECTED REDUCED HESSIAN ALGORITHM WITH TWO-PIECE UPDATE FOR CONSTRAINED OPTIMIZATION

This paper proposes a two-piece update of projected reduced Hessian algorithm with nonmonotonic trust region strategy for solving nonlinear equality constrained optimization problems. In order to deal with large problems, a two-piece update of twoside projected reduced Hessian is used to replace full Hessian matrix. By adopting the Fletcher's penalty function as the merit function, a nonmonotonic trust region strategy is suggested which does not require the merit function to reduce its value in every iteration. The two-piece update of projected reduced Hessian algorithm which switches to nonmonotonic trust region technique possesses global convergence while maintaining a two-step Q-superlinear local convergence rate under some reasonable conditions. Furthermore, one step Q-superlinear local convergence rate can be obtained if at least one of the update formulas is updated at each iteration by an alternative update rule. The numerical experiment results are reported to show the effectiveness of the propo     

基于MQNM的双基地雷达目标定位改进算法

针对求解双基地雷达目标定位问题常用的Gauss-Newton法自身固有的缺点,如收敛精度和收敛速度依赖于迭代初值与真实值的接近程度和函数的非线性程度,进一步考虑了目标函数Hessian阵的二阶信息,结合MQNM法(修正拟牛顿法)提出了一种双基地雷达目标定位问题的优化改进算法。计算机仿真结果表明了该算法的可行性和有效性。     

AN ADAPTIVE TRUST REGION METHOD FOR EQUALITY CONSTRAINED OPTIMIZATION

In this paper, a trust region method for equality constrained optlmization based on nondiferentiable exact penalty is proposed. In this algorithin, the trail step is characterized by computation of its normal component being separated from computation of its tangential component, i.e., only the tangential component of the trail step is constrained by trust radius while the normal component and trail step itself have no constraints. The other main characteristic of the algorithm is the decision of trust region radius. Here, the decision of trust region radius uses the information of the gradient of objective function and reduced Hessian. However, Maratos effect will occur when we use the nondifferentiable exact penalty function as the merit function. In order to obtain the superlinear convergence of the algorithm, we use the twice order correction technique. Because of the speciality of the adaptive trust region method, we use twice order correction when p= 0 (the definition is as in Section 2) and this is different from the traditional trust region methods for equality constrained opthnization. So the computation of the algorithm in this paper is reduced. What is more, we can prove that the algorithm is globally and superlinearly convergent.     

Nonmonotonic Reduced Projected Hessian Method Via an Affine Scaling Interior Modified Gradient Path for Bounded-Constrained Optimization

The authors propose an affine scaling modified gradient path method in association with reduced projective Hessian and nonmonotonic interior backtracking line search techniques for solving the linear equality constrained optimization subject to bounds on variables. By employing the QR decomposition of the constraint matrix and the eigensystem decomposition of reduced projective Hes- sian matrix in the subproblem, the authors form affine scaling modified gradient curvilinear path very easily. By using interior backtracking line search technique, each iterate switches to trial step of strict interior feasibility. The global convergence and fast local superlinear/quadratical convergence rates of the proposed algorithm are established under some reasonable conditions. A nonmonotonic criterion should bring about speeding up the convergence progress in some ill-conditioned cases. The results of numerical experiments are reported to show the effectiveness of the proposed algorithm.     

一种变阶数自适应滤波算法

通过对回声抵消的实际应用环境进行分析,提出一种新的动态改变自适应滤波器阶数的算法。该算法在权系数的长度与失调误差信号之间建立一种非线性函数关系,具有在环境突变阶段,保持较高的滤波器阶数,而在稳态阶段自动减少阶数的特点,可以极大地降低自适应滤波器算法的运算量。理论分析和计算机仿真结果表明,该算法具有良好的收敛性能和跟踪性能,稳态误差的水平与传统算法保持一致。     

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.     

存在基站误差的稳健时差定位算法

针对存在基站误差的目标无源定位问题,提出了一种基于修正牛顿算法的时差定位技术。众所周知,牛顿法对初值要求较高,较差初值会导致迭代发散,而且基站位置误差也会导致牛顿算法Hessian矩阵维数扩大和目标函数的缓慢下降,使运算量变大。该算法利用最大似然方法确定目标函数,运用牛顿法对目标位置进行迭代求解,对于计算过程中可能出现的病态Hessian矩阵,引入正则化理论修正病态的Hessian矩阵,使保证迭代收敛,同时简化算法降低Hessian矩阵的维数并且加速目标函数的下降趋势,使目标位置解脱离局部最小值,算法能够稳健高效的运行。实验结果表明:相对于传统牛顿法,此算法在初始值的选取上具有稳健性,对误差选取较大的初始值,仍能够保证算法的收敛性,同时加速了收敛速度,降低了计算量;相对于现有闭合式定位方法,此算法在噪声较大时具有较好的定位精度。     

基于加速度信息的导航卫星轨控期间自主定轨方法

为了降低对地面测控站的依赖,提升导航卫星自身的自主运行能力具有重要意义。导航卫星在轨道控制期间,自主定轨误差将会产生重大偏差,为了能够快速恢复星历,提升导航系统的应用效率,针对导航卫星轨控期间的自主轨道确定技术进行了研究。首先,在传统的天文导航的基础上引入了加速度信息,然后根据加速度计测量以及估计误差判断,选择合适的时机在轨控期间对估计误差方差阵进行重置。仿真结果表明,基于加速度信息的自适应导航滤波算法,能够有效降低导航误差收敛时间,同时降低估计误差峰值。     

Modelling of a Class of Nonstationary Time Series with Kalman Filter Using Moving Window

In this paper a method for modelling and forecasting of a class of nonstationary time series with Kalmnan filter using moving window is proposed. The procedure of the method is as follows: in terms of parameter estimation during recursive process by using LSM, the state space equation is constructed, then the Kahnan filter using moving window is made to get the data with reduced level of observation noise. Finally, the precise parameter estimation can be obtained by using the LSM again. The algorithm is carried on recursively. Good results for estimating and forecasting are shown by simulation, examples. The algorithm of Kalman filter using moving window proposed by us is introduced in this paper, which can guarantee the precision and convergence of Kalman filter.     

卫星信道中基于部分解耦的volterra均衡算法

对信道中大功率放大器产生的非线性特性实现快速有效地均衡是提高卫星通信系统性能关键技术之一。文中首先建立了基于volterra级数的卫星信道模型,并分析了信道对二维调制信号所产生的非线性影响;针对基于最小均方误差实现的volterra均衡器收敛速度慢这一问题,提出了基于复基带volterra模型的部分解耦均衡算法,该算法使均衡器线性权系数收敛于线性滤波器最优解,并用拉格朗日乘数法构造了新的代价函数,使均衡器的各阶权系数满足约束,以达到均衡器各阶权系数之间的解耦。仿真结果表明,新算法在保证稳态误差的条件下,其收敛所需迭代次数相对于全耦合的最小均方误差算法从16 000次减小到1 000次。     

基于洛伦兹函数的变步长凸组合最小均方算法

为进一步减小收敛速率与稳态误差之间的矛盾,改善自适应滤波算法,利用改进的Lorentzian函数提出了一种新的变步长凸组合最小均方(new variable step-size convex combination of least mean square,NVS-CLMS)算法,该算法既有效提高了收敛速率又具备很好的抗干扰能力。同时,为了克服CLMS算法停滞等待的弊端,采用了瞬时转移结构;另外,在参数的迭代公式中使用sign函数进行优化以降低运算量。仿真结果证明该算法与CLMS、VS-CLMS相比,在不同的仿真环境中均能表现出良好的均方特性和跟踪特性。     

Optimal design study of high order FIR digital filters based on neural network algorithm

An optimal design approach of high order FIR digital filter is developed based on the algorithm of neural networks with cosine basis function . The main idea is to minimize the sum of the square errors between the amplitude response of the desired FIR filter and that of the designed by training the weights of neural networks, then obtains the impulse response of FIR digital filter . The convergence theorem of the neural networks algorithm is presented and proved, and the optimal design method is introduced by designing four kinds of FIR digital filters , i.e., low-pass, high-pass, bandpass , and band-stop FIR digital filter. The results of the amplitude responses show that attenuation in stop-bands is more than 60 dB with no ripple and pulse existing in pass-bands, and cutoff frequency of passband and stop-band is easily controlled precisely .The presented optimal design approach of high order FIR digital filter is significantly effective.     

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…     

一种多尺度圆形滤波器在肺结节增强中的应用

肺部CT图像的结节检测由于受到噪声和肺部区域中气管、血管的干扰,一直是医学辅助诊断领域中的一个难点。针对这一问题,提出了一种基于多尺度的各向异性平滑方程的圆形滤波器方法。该方法首先利用各向异性平滑方程与高斯圆模型的Hessian矩阵推导出多尺度的圆形平滑方程,利用该方程对结节图像进行多尺度平滑;然后分析了高斯圆模型Hessian矩阵特征值的特点,建立了圆形增器滤波函数。最后,利用该滤波函数对多尺度平滑后的结节图像进行圆形增强滤波。实验证明该方法能够有效地抑止非圆形状的干扰,得到较好的结节增强图像,为后续的结节特征提取与分类奠定了基础。     

EQUILIBRIUM ALGORITHMS WITH NONMONOTONE LINE SEARCH TECHNIQUE FOR SOLVING THE TRAFFIC ASSIGNMENT PROBLEMS

This paper presents a unified bination algorithms （such as FrankWolfe problems. Global convergence results are framework of the nonmonotone convex comAlgorithm） for solving the traffic assignment established under mild conditions. The line search procedure used in our algorithm includes the nonmonotone Armijo rule, the non- monotone Goldstein rule and the nonmonotone Wolfe rule as special cases. So, the new algorithm can be viewed as a generalization of the regular convex combination algorithm.     

KF/UPF在SINS大方位失准角初始对准中的应用

为解决捷联惯导系统大方位失准角初始对准中状态维数较高,直接应用无迹粒子滤波(unscented particle filter, UPF)会带来维数灾难的问题,提出了基于卡尔曼滤波(Kalman filter, KF) /UPF组合滤波的初始对准方法。将非线性初始对准模型分解为线性与非线性两部分,采用KF实现对线性部分的最优估计,采用UPF对系统的非线性部分进行状态估计。通过仿真比较不同粒子数下KF/UPF组合滤波算法和UPF算法,结果表明,KF/UPF组合滤波算法在保证初始对准精度和收敛速度的同时,将需要进行UPF滤波的状态维数由10 维降为3 维,减少了计算量,运算时间分别缩短至原来的52.69%和6.0%,提高了初始对准的实时性。     

基于自适应CKF的恒模盲波束形成算法

针对均匀线阵,利用信号的恒模特性,与容积卡尔曼滤波相结合,提出一种新的盲自适应波束形成算法。通过对恒模算法的优化代价函数进行变换,使其满足系统状态空间模型。利用容积卡尔曼滤波算法进行自适应滤波,以实现抑制干扰和消除噪声。所提算法对状态空间模型中的系统噪声和过程噪声进行了自适应处理,免除滤波噪声参数的设置,增强了算法的通用性,并引入了收敛因子,加速系统的收敛速度。仿真结果表明了该算法的正确性和有效性。     

考虑缺货和缺陷品的模糊生产库存模型的优化求解

提出了一种同时考虑缺货和缺陷品的生产库存模型,并利用模糊集理论进行优化求解.用梯形模糊数来描述各变量,并采用梯级平均综合表示法对目标函数进行解模糊.采用扩展拉格朗日法与反证法相结合的方法,解决了不等式约束下的目标函数的求解问题.Hessian矩阵的正定特性证明了目标函数在最佳生产量处存在最小的生产库存总成本.最后通过数据分析,研究了缺陷率和缺货对生产量和生产库存总成本的影响.