• 대한전기학회:학술대회논문집
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• 대한전기학회 1991년도 추계학술대회 논문집 학회본부
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• pp.35-38
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• 1991

Recent, problems on the voltage-instability have been paid attention in power system and methods to find the limit of voltage-stability, concerned with these problems, were developed. However, these methods are short of precision on the limit of voltage-instability. Here, using the second-order load flow, constraint equation(d Pi/d Vi=0) and its patial differentiations are precisely formulated. Also, since the taylor series expansion of power flow equations terminates at the second-order terms, partial differentiations of constraint equation, that is Hessian, are constant. Then, Hessian matrix are calculated once during iteration process.

• International Journal of Aeronautical and Space Sciences
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• 제11권1호
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• pp.10-18
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• 2010

The purpose of this paper deals with direct multiple-shooting method (DMS) to resolve helicopter maneuver problems of helicopters. The maneuver problem is transformed into nonlinear problems and solved DMS technique. The DMS method is easy in handling constraints and it has large convergence radius compared to other strategies. When parameterized with piecewise constant controls, the problems become most effectively tractable because the search direction is easily estimated by solving the structured Karush-Kuhn-Tucker (KKT) system. However, generally the computation of function, gradients and Hessian matrices has considerably time-consuming for complex system such as helicopter. This study focused on the approximation of the KKT system using the matrix exponential and its integrals. The propose method is validated by solving optimal control problems for the linear system where the KKT system is exactly expressed with the matrix exponential and its integrals. The trajectory tracking problem of various maneuvers like bob up, sidestep near hovering flight speed and hurdle hop, slalom, transient turn, acceleration and deceleration are analyzed to investigate the effects of algorithmic details. The results show the matrix exponential approach to compute gradients and the Hessian matrix is most efficient among the implemented methods when combined with the mixed time integration method for the system dynamics. The analyses with the proposed method show good convergence and capability of tracking the prescribed trajectory. Therefore, it can be used to solve critical areas of helicopter flight dynamic problems.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제11권4호
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• pp.39-46
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• 2007

One of well known and much studied nonlinear matrix equations is the matrix polynomial which has the form G(X)=$A_0X^m+A_1X^{m-1}+{\cdots}+A_m$ where $A_0$, $A_1$, ${\cdots}$, $A_m$ and X are $n{\times}n$ real matrices. We show how the minimization methods can be used to solve the matrix polynomial G(X) and give some numerical experiments. We also compare Polak and Ribi$\acute{e}$re version and Fletcher and Reeves version of conjugate gradient method.

• Journal of the Optical Society of Korea
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• 제18권4호
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• pp.317-329
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• 2014

In vision measurement systems based on structured light, the key point of detection precision is to determine accurately the central position of the projected laser line in the image. The purpose of this research is to extract laser line centers based on a decision function generated to distinguish the real centers from candidate points with a high recognition rate. First, preprocessing of an image adopting a difference image method is conducted to realize image segmentation of the laser line. Second, the feature points in an integral pixel level are selected as the initiating light line centers by the eigenvalues of the Hessian matrix. Third, according to the light intensity distribution of a laser line obeying a Gaussian distribution in transverse section and a constant distribution in longitudinal section, a normalized model of Hessian matrix eigenvalues for the candidate centers of the laser line is presented to balance reasonably the two eigenvalues that indicate the variation tendencies of the second-order partial derivatives of the Gaussian function and constant function, respectively. The proposed model integrates a Gaussian recognition function and a sinusoidal recognition function. The Gaussian recognition function estimates the characteristic that one eigenvalue approaches zero, and enhances the sensitivity of the decision function to that characteristic, which corresponds to the longitudinal direction of the laser line. The sinusoidal recognition function evaluates the feature that the other eigenvalue is negative with a large absolute value, making the decision function more sensitive to that feature, which is related to the transverse direction of the laser line. In the proposed model the decision function is weighted for higher values to the real centers synthetically, considering the properties in the longitudinal and transverse directions of the laser line. Moreover, this method provides a decision value from 0 to 1 for arbitrary candidate centers, which yields a normalized measure for different laser lines in different images. The normalized results of pixels close to 1 are determined to be the real centers by progressive scanning of the image columns. Finally, the zero point of a second-order Taylor expansion in the eigenvector's direction is employed to refine further the extraction results of the central points at the subpixel level. The experimental results show that the method based on this normalization model accurately extracts the coordinates of laser line centers and obtains a higher recognition rate in two group experiments.

• 한국전산구조공학회논문집
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• 제20권6호
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• pp.751-759
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• 2007

저자는 기존의 연구에서 대용량-비선형성을 가지는 유체의 최적화를 수행하기 위해 몇 가지 강력한 방법들을 제시한 바 있다. 즉, 최적화 과정에서 수렴성을 높이기 위해 step by step기법을 사용하였고, 또한 수렴속도를 높이기 위하여 최적화이터레이션 과정에서 얻어지는 민감도정보를 이용하여 시스템 평형방정식의 해석을 위한 좋은 초기치를 제공하는 방법과, 평형방정식을 구속조건으로 사용하는 동시기법(simultaneous technique)에서 착안하여 해석과 최적화 수렴 판정치를 조작하는 방법을 제시한 바 있다. 그러나 그들 기법은 기본적으로 유사뉴턴법에 기본을 두고 있다. 현재까지 최적화에서 SQP기법을 사용할 때는 정확한 헤시안 매트릭스의 유도가 매우 까다롭고 힘들기 때문에 유사뉴턴법을 사용하고 있는 실정이다. 그러나 3차원 문제와 같이 더욱 큰 용량의 문제를 위해서는 진정한 의미에서의 뉴턴법, 트루 뉴턴법(true Newton method)을 사용할 필요가 있다. 본 연구에서는 트루 뉴턴법을 사용하기 위해 헤시안 매트릭스의 정확치를 얻는 과정을 유도하고 이를 기본으로 트루 뉴턴법을 이용한 최적화 루틴을 만들었다. 그리고 이를 3차원 문제에 적용하여 그 효과를 검증하였다.

• Journal of applied mathematics & informatics
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• 제17권1_2_3호
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• pp.401-418
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• 2005

In this paper, a dual algorithm, based on a smoothing function of Bertsekas (1982), is established for solving unconstrained minimax problems. It is proven that a sequence of points, generated by solving a sequence of unconstrained minimizers of the smoothing function with changing parameter t, converges with Q-superlinear rate to a Kuhn-Thcker point locally under some mild conditions. The relationship between the condition number of the Hessian matrix of the smoothing function and the parameter is studied, which also validates the convergence theory. Finally the numerical results are reported to show the effectiveness of this algorithm.

• Journal of the Korean Data and Information Science Society
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• 제14권3호
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• pp.451-459
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• 2003

The present paper suggests a method to estimate confidence interval using SV(Support Vector) in LS-SVM(Least-Squares Support Vector Machine). To get the proposed method we used the fact that the values of the hessian matrix obtained by full data set and SV are not different significantly. Since the suggested method implement only SV, a part of full data, we can save computing time and memory space. Through simulation study we justified the proposed method.

• Journal of applied mathematics & informatics
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• 제16권1_2호
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• pp.195-205
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• 2004

To the unconstrained programme of non-convex function, this article give a modified BFGS algorithm. The idea of the algorithm is to modify the approximate Hessian matrix for obtaining the descent direction and guaranteeing the efficacious of the quasi-Newton iteration pattern. We prove the global convergence properties of the algorithm associating with the general form of line search, and prove the quadratic convergence rate of the algorithm under some conditions.

• 에너지공학
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• 제10권3호
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• pp.183-187
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• 2001

Impedance imaging for binary mixture is a kind of nonlinear inverse problem, which is usually solved iteratively by the Newton-Raphson method. Then, the ill-posedness of Hessian matrix often requires the use of a regularization method to stabilize the solution. In this study, the Levenberg-Marquredt regularization method is introduced for the binary-mixture system with various resistivity contrasts (1:2∼1:1000). Several mixture distribution are tested and the results show that the Newton-Raphson iteration combined with the Levenberg-Marquardt regularization can reconstruct reasonably good images.

• 호남수학학술지
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• 제27권3호
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• pp.477-485
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• 2005

Let ($M^n$, g) be a compact oriented Riemannian manifold. It has been conjectured that every solution of the equation $z_g=D_gdf-{\Delta}_gfg-fr_g$ is an Einstein metric. In this article, we deal with the 3 dimensional case of the equation. In dimension 3, if the conjecture fails, there should be a stable minimal hypersurface in ($M^3$, g). We study some necessary conditions to guarantee that a stable minimal hypersurface exists in $M^3$.