• Journal of applied mathematics & informatics
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• v.6 no.3
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• pp.747-756
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• 1999

The Newtom method and the quasi-Newton method for solving equations of smooth compositions of semismooth functions are proposed. The Q-superlinear convergence of the Newton method and the Q-linear convergence of the quasi-Newton method are proved. The present methods can be more easily implemeted than previous ones for this class of nonsmooth equations.

• Journal of the Korean Mathematical Society
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• v.33 no.4
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• pp.865-878
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• 1996

We consider numerical methods for finding a solution to a nonlinear system of algebraic equations $$ (1) f(x) = 0, $$ where the function $f : R^n \to R^n$ is ain $x \in R^n$. In [10], a quasi-Gauss-Newton method is proposed and shown the computational efficiency over SQRT algorithm by numerical experiments. The convergence rate of the method has not been proved theoretically. In this paper, we show theoretically that the iterate $x_k$ obtained from the quasi-Gauss-Newton method for the problem (1) actually converges to a root by Kantorovich-type convergence analysis. We also show the rate of convergence of the method is superlinear.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.66 no.7
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• pp.1053-1058
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• 2017

In this paper, the design of iron loss minimization of 600W was performed by using Quasi-Newton method. Stator shoe, the width of stator teeth and yoke, and the length of d-axis flux path were selected as design parameters, and the output characteristics according to each design variable were considered. The objective function was set to minimize iron loss. Using the Quasi-Newton method, the variables converged to the target value while changing simultaneously and multiple times. As the algorithm advanced optimization, the correlation with the behavior of each variable was compared and analyzed.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.7 no.1
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• pp.7-14
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• 2003

The main concern of this paper is to develop a new class of quasi-newton methods. These methods are intended for use whenever memory space is a major concern and, hence, they are usually referred to as limited memory methods. The methods developed in this work are sensitive to the choice of the memory parameter ${\eta}$ that defines the amount of past information stored within the Hessian (or its inverse) approximation, at each iteration. The results of the numerical experiments made, compared to different choices of these parameters, indicate that these methods improve the performance of limited memory quasi-Newton methods.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.361-367
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• 2007

In this paper we propose an implementable method for solving a nonsmooth convex optimization problem by combining Moreau-Yosida regularization, bundle and quasi-Newton ideas. The method we propose makes use of approximate subgradients of the objective function, which makes the method easier to implement. We also prove the convergence of the proposed method under some additional assumptions.

• 제어로봇시스템학회:학술대회논문집
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• 2004.08a
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• pp.32-35
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• 2004

In boundary estimation in Electrical Impedance Tomography (EIT), conventional method is the modified Newton Raphson (mNR) method .The mNR is famous for good method since has good convergence and robustness against noisy data. But the mNR is low efficiency to get and update Jacobian matrix. So, the mNR become very slow algorithm. We propose the Quasi Newton (QN) method to improve efficiency which will lead to speed up in boundary estimation. The QN can improve a low efficiency by using estimated Jacobian matrix contrary to using exactly calculated Jacobian matrix, this used by the mNR. And finally, we propose the modified Quasi Newton (mQN) method because the QN has some problems such as bad early convergence rate and instability of 'divided by zero'. For the verification of the propose method, numerical experiments are conducted and the results show a good performance.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.66 no.5
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• pp.772-777
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• 2017

In this paper, the goal of optimization design is efficiency increase and vibration optimization. For this purpose, shape optimization design was performed using Quasi-Newton method, which is one of optimization techniques, and it was verified through finite element analysis In addition, modal analysis of the stator was performed to estimate the natural frequency. through the vibration experiment, the vibration was verified for cogging torque and RMF analysis. Finally, optimal and basic models were compared and analyzed for efficeincy characteristics.

• Transactions on Electrical and Electronic Materials
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• v.6 no.6
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• pp.256-261
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• 2005

This paper presents that the modeling to predict the characteristics with respect to the performance of solenoid embedded inductors manufactured by LTCC process via the nonlinear regression model based on the quasi-Newton method. In order to reduce the runs, the design of experiments (DOE) was used to generate the design space. The nonlinear process models were constructed by the piecewise regression model based on the quasi-Newton method for estimating the model coefficient with the break point on the statistical confidence intervals. Those models were verified by the model accuracy checking based on the assumption statistically.

• Journal of the Korean Mathematical Society
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• v.53 no.6
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• pp.1371-1389
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• 2016

In this paper, we propose a new rank two quasi-Newton method based on adjoint Broyden updates for solving symmetric nonlinear equations, which can be seen as a class of adjoint BFGS method. The new rank two quasi-Newton update not only can guarantee that $B_{k+1}$ approximates Jacobian $F^{\prime}(x_{k+1})$ along direction $s_k$ exactly, but also shares some nice properties such as positive deniteness and least change property with BFGS method. Under suitable conditions, the proposed method converges globally and superlinearly. Some preliminary numerical results are reported to show that the proposed method is effective and competitive.

• Communications of the Korean Mathematical Society
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• v.9 no.2
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• pp.491-502
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• 1994

Many problems arising in science and engineering require the numerical solution of a system of n nonlinear equations in n unknowns: (1) given F : $R^{n}$ $\rightarrow$ $R^{n}$ , find $x_{*}$ $\epsilon$ $R^{n}$ / such that F($x_{*}$) = 0. Nonlinear problems are generally solved by iteration. Davidson [3] and Broyden [1] introduced the methods which had led to a large amount of research and a class of algorithm. This work has been called by the quasi-Newton methods, secant updates, or modification methods. Newton's method is the classical method for the problem (1) and quasi-Newton methods have been proposed to circumvent computational disadvantages of Newton's method.(omitted)