3D magnetotelluric inversions with unstructured finite-element and limited-memory quasi-Newton methods

Traditional 3D Magnetotelluric(MT) forward modeling and inversions are mostly based on structured meshes that have limited accuracy when modeling undulating surfaces and arbitrary structures. By contrast, unstructured-grid-based methods can model complex underground structures with high accuracy and overcome the defects of traditional methods, such as the high computational cost for improving model accuracy and the difficulty of inverting with topography. In this paper, we used the limited-memory quasi-Newton(L-BFGS) method with an unstructured finite-element grid to perform 3D MT inversions. This method avoids explicitly calculating Hessian matrices, which greatly reduces the memory requirements. After the first iteration, the approximate inverse Hessian matrix well approximates the true one, and the Newton step(set to 1) can meet the sufficient descent condition. Only one calculation of the objective function and its gradient are needed for each iteration, which greatly improves its computational efficiency. This approach is well-suited for large-scale 3D MT inversions. We have tested our algorithm on data with and without topography, and the results matched the real models well. We can recommend performing inversions based on an unstructured finite-element method and the L-BFGS method for situations with topography and complex underground structures.

BFGS quasi-Newton location algorithm using TDOAs and GROAs

With the emergence of location-based applications in various fields, the higher accuracy of positioning is demanded. By utilizing the time differences of arrival （TDOAs） and gain ratios of arrival （GROAs）, an efficient algorithm for estimating the position is proposed, which exploits the Broyden-Fletcher-Goldfarb-Shanno （BFGS） quasi-Newton method to solve nonlinear equations at the source location under the additive measurement error. Although the accuracy of two-step weighted-least-square （WLS） method based on TDOAs and GROAs is very high, this method has a high computational complexity. While the proposed approach can achieve the same accuracy and bias with the lower computational complexity when the signal-to-noise ratio （SNR） is high, especially it can achieve better accuracy and smaller bias at a lower SNR. The proposed algorithm can be applied to the actual environment due to its real-time property and good robust performance. Simulation results show that with a good initial guess to begin with, the proposed estimator converges to the true solution and achieves the Cramer-Rao lower bound （CRLB） accuracy for both near-field and far-field sources.

FPGA-based Acceleration of Davidon-Fletcher-Powell Quasi-Newton Optimization Method

Quasi-Newton methods are the most widely used methods to find local maxima and minima of functions in various engineering practices. However, they involve a large amount of matrix and vector operations, which are computationally intensive and require a long processing time. Recently, with the increasing density and arithmetic cores, field programmable gate array(FPGA) has become an attractive alternative to the acceleration of scientific computation. This paper aims to accelerate Davidon-Fletcher-Powell quasi-Newton(DFP-QN) method by proposing a customized and pipelined hardware implementation on FPGAs. Experimental results demonstrate that compared with a software implementation, a speed-up of up to 17 times can be achieved by the proposed hardware implementation.

GLOBAL COVERGENCE OF THE NON-QUASI-NEWTON METHOD FOR UNCONSTRAINED OPTIMIZATION PROBLEMS

In this paper, the non-quasi-Newton＇s family with inexact line search applied to unconstrained optimization problems is studied. A new update formula for non-quasi-Newton＇s family is proposed. It is proved that the constituted algorithm with either Wolfe-type or Armijotype line search converges globally and Q-superlinearly if the function to be minimized has Lipschitz continuous gradient.

A Quasi-Newton Neural Network Based Efficient Intrusion Detection System for Wireless Sensor Network

In Wireless Sensor Networks(WSN),attacks mostly aim in limiting or eliminating the capability of the network to do its normal function.Detecting this misbehaviour is a demanding issue.And so far the prevailing research methods show poor performance.AQN3 centred efficient Intrusion Detection Systems(IDS)is proposed in WSN to ameliorate the performance.The proposed system encompasses Data Gathering(DG)in WSN as well as Intrusion Detection(ID)phases.In DG,the Sensor Nodes(SN)is formed as clusters in the WSN and the Distance-based Fruit Fly Fuzzy c-means(DFFF)algorithm chooses the Cluster Head(CH).Then,the data is amassed by the discovered path.Next,it is tested with the trained IDS.The IDS encompasses‘3’steps:pre-processing,matrix reduction,and classification.In pre-processing,the data is organized in a clear format.Then,attributes are presented on the matrix format and the ELDA(entropybased linear discriminant analysis)lessens the matrix values.Next,the output as of the matrix reduction is inputted to the QN3 classifier,which classifies the denial-of-services(DoS),Remotes to Local(R2L),Users to Root(U2R),and probes into attacked or Normal data.In an experimental estimation,the proposed algorithm’s performance is contrasted with the prevailing algorithms.The proposed work attains an enhanced outcome than the prevailing methods.

Quasi-Newton Method for Optimal Blank Allowance Balancing

A balancing technique for casting or forging parts to be machined is presented in this paper.It allows an optimal part setup to make sure that no shortage of material(undercut)will occur during machining.Particularly in the heavy part in- dustry,where the resulting casting size and shape may deviate from expectations,the balancing process discovers whether or not the design model is totally enclosed in the actual part to be machined.The alignment is an iterative process involving nonlinear con- strained optimization,which forces data points to lie outside the nominal model under a specific order of priority.Newton methods for non-linear numerical minimization are rarely applied to this problem because of the high cost of computing.In this paper, Newton methods are applied to the balancing of blank part.The aforesaid algorithm is demonstrated in term of a marine propeller blade,and result shows that The Newton methods are more efficient and accurate than those implemented in past research and have distinct advantages compared to the registration methods widely used today.

OPTIMAL MOTION PLANNING FOR A RIGID SPACECRAFT WITH TWO MOMENTUM WHEELS USING QUASI-NEWTON METHOD

An optimal motion planning scheme based on the quasi-Newton method is proposed for a rigid spacecraft with two momentum wheels. A cost functional is introduced to incorporate the control energy, the final state errors and the constraints on states. The motion planning for determining control inputs to minimize the cost functional is formulated as a nonlinear optimal control problem. Using the control parametrization, one can transform the infinite dimensional optimal control problem to a finite dimensional one that is solved via the quasi-Newton methods for a feasible trajectory which satisfies the nonholonomic constraint. The optimal motion planning scheme was applied to a rigid spacecraft with two momentum wheels. The simulation results show the effectiveness of the proposed optimal motion planning scheme.

Studies on quasi-Newton methods in timedomain multiscale full waveform inversion

The time-domain multiscale full waveform inversion(FWI)mitigates the influence of the local minima problem in nonlinear inversion via sequential inversion using different frequency components of seismic data.The quasi-Newton methods avoid direct computation of the inverse Hessian matrix,which reduces the amount of computation and storage requirement.A combination of the two methods can improve inversion accuracy and efficiency.However,the quasi-Newton methods in time-domain multiscale FWI still cannot completely solve the problem where the inversion is trapped in local minima.We first analyze the reasons why the quasi-Newton Davidon–Fletcher–Powell and Broyden–Fletcher–Goldfarb–Shanno methods likely fall into the local minima using numerical experiments.During seismic-wave propagation,the amplitude decreases with the geometric diffusion,resulting in the concentration of the gradient of the velocity model in the shallow part,and the deep velocity cannot be corrected.Thus,the inversion falls into the local minima.To solve this problem,we introduce a virtual-source precondition to remove the influence of geometric diffusion.Thus,the model velocities in the deep and shallow parts can be simultaneously completely corrected,and the inversion can more stably converge to the global minimum.After the virtual-source precondition is implemented,the problem in which the quasi-Newton methods likely fall into the local minima is solved.However,problems remain,such as incorrect search direction after a certain number of iterations and failure of the objective function to further decrease.Therefore,we further modify the process of timedomain multiscale FWI based on virtual-source preconditioned quasi-Newton methods by resetting the inverse of the approximate Hessian matrix.Thus,the validity of the search direction of the quasi-Newton methods is guaranteed.Numerical tests show that the modified quasi-Newton methods can obtain more reasonable inversion results,and they converge faster and entail lesser computational resources than the gradient method.

An Improved Quasi-Newton Method for Unconstrained Optimization

We present an improved method. If we assume that the objective function is twice continuously differentiable and uniformly convex, we discuss global and superlinear convergence of the improved quasi-Newton method.

A Study of BCI Signal Pattern Recognition by Using Quasi-Newton-SVM Method

The recognition of electroencephalogram (EEG) signals is the key of brain computer interface (BCI). Aimed at the problem that the recognition rate of EEG by using support vector machine (SVM) is low in BCI, based on the assumption that a well-defined physiological signal which also has a smooth form "hides" inside the noisy EEG signal, a Quasi-Newton-SVM recognition method based on Quasi-Newton method and SVM algorithm was presented. Firstly, the EEG signals were preprocessed by Quasi-Newton method and got the signals which were fit for SVM. Secondly, the preprocessed signals were classified by SVM method. The present simulation results indicated the Quasi-Newton-SVM approach improved the recognition rate compared with using SVM method; we also discussed the relationship between the artificial smooth signals and the classification errors.

一种分解型Quasi-Newton电容层析成像图像重建算法

针对电容层析成像系统中的"软场"效应和病态问题,在分析电容层析成像和QuasiNewton算法原理的基础上,基于非线性最小二乘的成像原理,提出了一种新的分解型Quasi-Newton电容层析成像算法,推导出了求解ECT反问题的分解型拟牛顿图像重建算法放的计算步骤,同时利用信赖域公式对目标函数的Hessian矩阵进行校正.仿真实验表明,基于分解型拟牛顿方法具有可行性,对于基本流型该算法与LBP算法相比,具有成像质量高和边界均匀稳定的特点,为ECT图像重建的研究提供了一个新的思路.

一种μGA+Quasi-Newton的混合优化算法

提出了一种新型的优化算法。此算法利用微种群遗传算法(μGA)的全局最优性在大范围内搜索可能的极值,而用拟牛顿(Quasi Newton)法的目标函数梯度下降特性在极值点附近快速搜索,从而实现了全局最优与快速搜索的有机结合。同时,通过几个典型的试验函数对此混合算法与微种群遗传算法的寻优效果做了比较。

A Switching Algorithm Based on Modified Quasi-Newton Equation

In this paper, a switching method for unconstrained minimization is proposed. The method is based on the modified BFGS method and the modified SR1 method. The eigenvalues and condition numbers of both the modified updates are evaluated and used in the switching rule. When the condition number of the modified SR1 update is superior to the modified BFGS update, the step in the proposed quasi-Newton method is the modified SR1 step. Otherwise the step is the modified BFGS step. The efficiency of the proposed method is tested by numerical experiments on small, medium and large scale optimization. The numerical results are reported and analyzed to show the superiority of the proposed method.

The Design of Circular Microstrip Patch Antenna by Using Quasi-Newton Algorithm of ANN

The paper presents the Quasi Newton model of Artificial Neural Network for design of circular microstrip antenna (MSA). In this model, a closed form expression is used for accurate determination of the resonant frequency of circular microstrip patch antenna. The calculated resonant frequency results are in good agreement with the experimental results reported elsewhere. The results show better agreement with the trained and tested data of ANN models. The results are verified by the experimental results to produce accurate ANN models. This presents ANN model practically as an alternative method to the detailed electromagnetic design of circular microstrip antenna.

ADAPTIVE REGULARIZED QUASI-NEWTON METHOD USING INEXACT FIRST-ORDER INFORMATION

Classical quasi-Newton methods are widely used to solve nonlinear problems in which the first-order information is exact.In some practical problems,we can only obtain approximate values of the objective function and its gradient.It is necessary to design optimization algorithms that can utilize inexact first-order information.In this paper,we propose an adaptive regularized quasi-Newton method to solve such problems.Under some mild conditions,we prove the global convergence and establish the convergence rate of the adaptive regularized quasi-Newton method.Detailed implementations of our method,including the subspace technique to reduce the amount of computation,are presented.Encouraging numerical results demonstrate that the adaptive regularized quasi-Newton method is a promising method,which can utilize the inexact first-order information effectively.

A GENERALIZED QUASI-NEWTON EQUATION AND COMPUTATIONAL EXPERIENCE

The quasi-Newton equation has played a central role in the quasi-Newton methods for solving systems of nonlinear equations and/or unconstrained optimization problems. Insteady Pan suggested a new equation, and showed that it is of the second order while the traditional of the first order, in certain approximation sense [12]. In this paper, we make a generalization of the two equations to include them as special cases. The generalized equation is analyzed, and new updates are derived from it. A DFP-like new update outperformed the traditional DFP update in computational experiments on a set of standard test problems.

A BI-LEVEL FORMULATION AND QUASI-NEWTON ALGORITHM FOR STOCHASTIC EQUILIBRIUM NETWORK DESIGN PROBLEM WITH ELASTIC DEMAND

In this paper, a bi-level formulation of the continuous network design problem (NDP) is proposed on the basis of logit stochastic user equilibrium (SUE) assignment with elastic demand. The model determines the link capacity improvements by maximizing net economic benefit while considering changes in demand and traffic distribution in network. The derivatives of equilibrium link flows and objective function with respect to capacity expansion variables, which are analytically derived, can be computed without having to first find path choice information. These derivatives are employed to develop a quasi Newton algorithm with the BFG S (Broyden- Fletcher- Goldfarb-Shanno) formula for solving the nonlinear, nonconvex but differentiable SUE-constrained network design problem. The SUE assignment with elastic demand is solved by using the method of successive averages in conjunction with Bell’s matrix inversion logit assignment method. Simple and complex example networks are presented to illustrate the model and the algorithm.

Quasi-Newton-type optimized iterative learning control for discrete linear time invariant systems

In this paper, a quasi-Newton-type optimized iterative learning control （ILC） algorithm is investigated for a class of discrete linear time-invariant systems. The proposed learning algorithm is to update the learning gain matrix by a quasi-Newton-type matrix instead of the inversion of the plant. By means of the mathematical inductive method, the monotone convergence of the proposed algorithm is analyzed, which shows that the tracking error monotonously converges to zero after a finite number of iterations. Compared with the existing optimized ILC algorithms, due to the superlinear convergence of quasi-Newton method, the proposed learning law operates with a faster convergent rate and is robust to the ill-condition of the system model, and thus owns a wide range of applications. Numerical simulations demonstrate the validity and effectiveness.

A CLASS OF FACTORIZED QUASI-NEWTON METHODS FOR NONLINEAR LEAST SQUARES PROBLEMS

This paper gives a class of descent methods for nonlinear least squares solution. A class of updating formulae is obtained by using generalized inverse matrices. These formulae generate an approximation to the second part of the Hessian matrix of the objective function, and are updated in such a way that the resulting approximation to the whole Hessian matrix is the convex class of Broyden-like up-dating formulae. It is proved that the proposed updating formulae are invariant under linear transformation and that the class of factorized quasi-Newton methods are locally and superlinearly convergent. Numerical results are presented and show that the proposed methods are promising.