• Journal of applied mathematics & informatics
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• v.16 no.1_2
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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.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.311-319
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• 2007

This article studies a modified BFGS algorithm for solving smooth unconstrained strongly convex minimization problem. The modified BFGS method is based on the new quasi-Newton equation $B_k+1{^s}_k=yk\;where\;y_k^*=yk+A_ks_k\;and\;A_k$ is a matrix. Wei, Li and Qi [WLQ] have proven that the average performance of two of those algorithms is better than that of the classical one. In this paper, we prove the global convergence of these algorithms associated to a general line search rule.

• Journal of the Earthquake Engineering Society of Korea
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• v.9 no.3 s.43
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• pp.23-32
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• 2005

Torsional behavior of eccentric structure under seismic leading may cause the stress and/or deformation concentration, which arouse the failure of the structure in an unexpected manner. This study suggests D-R relationship which shows the overall displacement and rotation of the system based on the ultimate displacement capacity of the each lateral load resistant member. Using the suggested D-R relationship and displacement spectrum, the seismic assessment is conducted and verified in comparison with the time history analysis result. Multi-level seismic assessment Is considered which takes multiple seismic hazard levels and respective performance levels into account. Finally, based on the seismic assessment result, seismic rehabilitation process is presented. In this research, two rehabilitation methods are considered. One is done by means of stiffening/strengthening the seismic resistant members, and the other is based on the member ductility. Especially, in the first method, to optimize the rehabilitation result, the rehabilitation problem is modeled as an optimization problem, and solved using BFGS quasi-Newton optimization method.

• Journal of Advanced Marine Engineering and Technology
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• v.24 no.1
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• pp.18-24
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• 2000

As ship's propulsion shafting system has been complicated, many linear methods that have been used until now are not sufficient enough to produce proper solutions and these solutions are ofter unreasonable. So we need to solve nonlinear systems, and many methods for solving nonlinear vibration system have been developed. In this study, the propulsion shafting system was modeled with Duffing's nonlinear vibration system and multi-degree-of-freedom, and analyzed by using Quasi-Newton method. And for the purpose of confirming the reliability of the calculating results for nonlinear forced torsional vibration of the propulsion shafting system, the nonlinear calculated results were compared with the linear calculated ones for ship's propulsion shafting system. In the result, for analysis of the forced torsional vibration of the propulsion systems with nonlinear elements, the modified Newton's method is confirmed reasonable.

• Journal of the Korean Data and Information Science Society
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• v.9 no.2
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• pp.219-225
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• 1998

The parameters in linear models with censored normal responses are usually estimated by the iterative maximum likelihood and least square methods. However, the iterative least square method is simple but hardly has theoretical justification, and the iterative maximum likelihood estimating equations are complicatedly derived. In this paper, we justify these methods via Wedderburn (1974)'s quasi-likelihood approach. This provides an explicit justification for the iterative least square method and also directly the iterative maximum likelihood method for estimating the regression coefficients.

• Journal of the Korean Statistical Society
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• v.27 no.3
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• pp.251-264
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• 1998

When the LRT is not feasible, we define quasi-LRT(QLRT) as a modification of the LRT Under some appropriate conditions the QLRT shares Bahadur optimality and Bartlett Adjustability with the LRT. When we can find maximum likelihood estimator under the null parameter space but not under the unrestricted parameter space, our QLRT is Bahadur optimal as is the LRT We suggest the stopping rule of the Newton-Raphson iterations for constructing the QLRT statistics which are Bartlett adjustable.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.325-331
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• 2007

To the unconstrained programme of non-convex function, this article give a modified BFGS algorithm associated with the general line search model. The idea of the algorithm is to modify the approximate Hessian matrix for obtaining the descent direction and guaranteeing the efficacious of the new quasi-Newton iteration equation $B_{k+1}s_k=y^*_k,\;where\;y^*_k$ is the sum of $y_k\;and\;A_ks_k,\;and\;A_k$ is some matrix. The global convergence properties of the algorithm associating with the general form of line search is proved.

• Journal of the Korean Institute of Telematics and Electronics
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• v.21 no.2
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• pp.8-12
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• 1984

Algorithms for solving a set of nonlinear simultaneous equations, which is frequently required in problems of controlling nonlinear processes, are proposed. Here the equation variables are first parameterized and a recursive identification technique is utilized. The forms and characteristics of the resultant algorithms are vary similar to the Broyden's quasi-Newton method, but their derivations and final recursion equations are different. Our methods possess almost all the merits of the Broyden's and numerical comparisons show our methods to be more efficient and reliable for some difficult problems.

• Proceedings of the Korea Water Resources Association Conference
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• 2010.05a
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• pp.679-683
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• 2010

본 연구에서는 공간적 변수인 조도계수를 기지의 수위값을 이용하여 최적값을 결정하는 방법에 대해서 검토하고자 한다. 최적화 기법에 의한 조도계수는 기지의 수위값과 수치모의에 의한 결과 값의 전체 오차를 최소화하는 값으로 결정된다. 본 연구에서는 3가지 최적화 기법을 이용하였으며 가상 수로에 대해서 적용하였다. 수위계산은 표준축차법에 의해 수행하였으며 사용된 최적화 기법은 quasi-Newton 방법이다. 1차원 모형은 Matlab을 이용하여 표준축자법으로 구성하였으며 BFGS 기법, L-BFGS 기법, Steepest Gradient Descent 기법 등도 Matlab으로 구성하였다. 표준축차법은 조도계수가 입력되면 기지의 수위값과의 2-norm을 계산하도록 구성하였다. 계산 결과에 의하면 세가 기법 모두 20 23회 정도의 반복계산을 수행하고 값이 수렴되었는데, L-BFGS의 경우에는 정확하게 음수의 조도계수로 수렴하였으며, BFGS기법과 Steepest Gradient 기법의 경우에는 양의 값으로 정확하게 수렴하였다.

• Proceedings of the Korea Water Resources Association Conference
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• 2008.05a
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• pp.640-644
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• 2008

하상경사가 커서 동수역학적 부정류 계산모형을 안정적으로 적용하기 어렵고, 홍수파의 감쇄효과가 적은 중소하천에 적합한 준정상류 계산모형을 개발하였다. 수립된 모형은 매 시각 유량에 대하여 1차원 하천 부등류 지배방정식인 단면 평균된 1차원 에너지 방정식을 풀도록 구성되어 있으며, 수치해법으로는 Newton-Raphson 방법을 적용한 표준축차법을 사용하였다. Newton-Raphson 방법을 적용하기 위해서는 통수면적, 하폭, 윤변, 동수반경 및 수위에 대한 윤변의 변화율 등의 변수들이 필요하다. 이와 같은 변수들은 각 계산점에서 수위를 계산하기에 앞서 단면자료를 사용하여 0.1 m 간격으로 모든 수위에 대하여 그 값들을 미리 구한 후, 반복 계산 단계에서 사용되는 수위에 대하여 필요한 변수들을 앞서 계산된 변수들과 선형 보간하여 사용하도록 하였다. 하천 구간내에 보가 존재하는 경우에는 보가 위치한 상 하류 간의 지배방정식으로 에너지 방정식 대신에 월류 유량 관계식을 사용하였으며, 이때의 수치해법 역시 Newton-Raphson 방법을 사용하였다. 수립된 모형을 한탄강 하류 구간에 적용하여 HEC-RAS 모형과 모의 결과를 비교한 결과, 두 모형의 계산결과가 잘 일치하는 것으로 나타났다. 에너지 경사항의 근사 방법에 따른 민감도 분석을 실시하였다.