• East Asian mathematical journal
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• 제25권2호
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• pp.153-157
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• 2009

Motivated by optimization considerations we revisit the work by Dontchev in [7] involving the convergence of Newton's method to a solution of a generalized equation in a Banach space setting. Using the same hypotheses and under the same computational cost we provide a finer convergence analysis for Newton's method by using more precise estimates.

• 한국전산구조공학회논문집
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• 제26권4호
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• pp.223-231
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• 2013

본 논문에서는 물성이 균일하지 않은 반무한 고체영역의 탄성파속도 분포를 재구성하기 위한 시간영역 Gauss-Newton 전체파형 역해석 기법을 소개한다. 반무한 영역을 유한 계산영역으로 치환하기 위하여 유한영역의 경계에 수치적 파동흡수 경계조건인 perfectly-matched-layers(PMLs)를 도입하였다. 이 역해석 문제는 PML을 경계로 하는 영역에서의 탄성파동방정식을 구속조건으로 하는 최적화 문제로 성립되며, 표면에서 측정된 변위응답과 혼합유한요소법에 의해 계산된 응답간의 차이를 최소화함으로써 미지의 탄성파속도 분포를 결정한다. 이 과정에서 Gauss-Newton-Krylov 최적화 알고리즘과 정규화기법을 사용하여 탄성파속도의 분포를 반복적으로 업데이트하였다. 1차원 수치예제들을 통해 Gauss-Newton 역해석으로 부터 재구성된 탄성파속도의 분포가 목표값에 충분히 근사함을 보였으며, Fletcher Reeves 최적화 알고리즘을 사용한 기존의 역해석 결과에 비해 수렴율이 현저히 개선되고 계산 소요시간이 단축됨을 확인할 수 있었다.

• 전기학회논문지
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• 제66권7호
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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.

• 전기학회논문지
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• 제67권10호
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• pp.1292-1297
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• 2018

In this paper, efficiency optimization design of 600W class IPMSM was performed by using Quasi-Newton method. The output was limited to 600W to meet the same output as the basic model. The behavior of each variable as the design progressed was judged on the efficiency, which is the target value through correlation analysis. The design variables were set as the width of the stator, the position of the permanent magnet from the end of the rotor, the thickness of the permanent magnet, and the width of the permanent magnet.

• 대한수학회보
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• 제53권6호
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• pp.1831-1844
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• 2016

In this paper, we improve the full-Newton step infeasible interior-point algorithm proposed by Mansouri et al. [6]. The algorithm takes only one full-Newton step in a major iteration. To perform this step, the algorithm adopts the largest logical value for the barrier update parameter ${\theta}$. This value is adapted with the value of proximity function ${\delta}$ related to (x, y, s) in current iteration of the algorithm. We derive a suitable interval to change the parameter ${\theta}$ from iteration to iteration. This leads to more flexibilities in the algorithm, compared to the situation that ${\theta}$ takes a default fixed value.

• 한국컴퓨터정보학회논문지
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• 제17권12호
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• pp.71-82
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• 2012

본 논문에서는 MCT(Modified Census Transform) 특징과 개선된 아다부스트 분류기를 이용한 번호판 검출 알고리즘을 제안한다. MCT 특징은 영상의 국소 지역 패턴을 정수화하여 표현하는 특징으로서 조명 변화에 강인하고 메모리 효율이 높은 장점이 있다. 그러나 패턴을 표현하는 정수형의 MCT 특징값들이 이산적인 특징을 가지기 때문에 아다부스트 훈련 방법을 적용하기 위해서는 룩업테이블 (Lookup Table)을 이용하여 분류기를 설계해야 한다. 그동안의 아다부스트 훈련 방법에 대한 최적화 연구는 지수 기준(exponential criterion)을 최소화 하는 방법에 대한 방향으로 연구가 진행되고 있다. 본 논문에서는 MCT 특징을 이용하고 지수 기준의 뉴턴 최적화를 통해 아다부스트 훈련 방법을 개선하여 번호판 검출성능을향상 시키는 방법을 제안한다. 번호판샘플 영상과 필드 테스트 영상에 대한 실험을 통해 제안한 방법의 성능을 고찰하고, 기존의 일반 아다부스트 훈련을 이용한 검출 방법과의 비교 실험을 통해 그 효용성을 입증한다.

• 한국정보과학회:학술대회논문집
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• 한국정보과학회 2004년도 가을 학술발표논문집 Vol.31 No.2 (2)
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• pp.697-699
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• 2004

Stochastic Neighbor Embedding(SNE) is a probabilistic method of mapping high-dimensional data space into a low-dimensional representation with preserving neighbor identities. Even though SNE shows several useful properties, the gradient-based naive SNE algorithm has a critical limitation that it is very slow to converge. To overcome this limitation, faster optimization methods should be considered by using trust region method we call this method fast TR SNE. Moreover, this paper presents a couple of useful optimization methods(i.e. conjugate gradient method and Newton's method) to embody fast SNE algorithm. We compared above three methods and conclude that TR-SNE is the best algorithm among them considering speed and stability. Finally, we show several visualizing experiments of TR-SNE to confirm its stability by experiments.

• Communications for Statistical Applications and Methods
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• 제12권2호
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• pp.443-451
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• 2005

The studied in this paper is a new algorithm for searching the maximum likelihood estimate(MLE) in which probability density function is not explicitly expressed. Newton-Raphson's root-finding routine and a nonlinear numerical optimization algorithm with constraint (so-called feasible sequential quadratic programming) are used. This algorithm is applied to the Wakeby distribution which is importantly used in hydrology and water resource research for analysis of extreme rainfall. The performance comparison between maximum likelihood estimates and method of L-moment estimates (L-ME) is studied by Monte-carlo simulation. The recommended methods are L-ME for up to 300 observations and MLE for over the sample size, respectively. Methods for speeding up the algorithm and for computing variances of estimates are discussed.

• Journal of applied mathematics & informatics
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• 제33권1_2호
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• pp.61-76
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• 2015

In this paper, a fifth order extension of Potra's third order iterative method is proposed for solving nonlinear equations. A convergence theorem along with the error bounds is established. The method takes three functions and one derivative evaluations giving its efficiency index equals to 1.495. Some numerical examples are also solved and the results obtained are compared with some other existing fifth order methods. Next, the interval extension of both third and fifth order Potra's method are developed by using the concepts of interval analysis. Convergence analysis of these methods are discussed to establish their third and fifth orders respectively. A number of numerical examples are worked out using INTLAB in order to demonstrate the efficacy of the methods. The results of the proposed methods are compared with the results of the interval Newton method.

• Journal of applied mathematics & informatics
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• 제32권5_6호
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• pp.747-760
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• 2014

In this paper a higher order iterative algorithm is developed for an unconstrained multivariate optimization problem. Taylor expansion of matrix valued function is used to prove the cubic order convergence of the proposed algorithm. The methodology is supported with numerical and graphical illustration.