• Journal of applied mathematics & informatics
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• v.5 no.3
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• pp.701-716
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• 1998

In this paper we develop algorithms in programming lan-guage SCHEME for implementation of the main first order gradient techniques for unconstrained optimization. Implementation of the de-scent techniques which use non-optimal descent steps as well as imple-mentation of the optimal descent techniques are described. Also we investigate implementation of the global problem called optimization along a line. Developed programs are effective and simpler with re-spect to the corresponding in the procedural programming languages. Several numerical examples are reported.

• Journal of computational fluids engineering
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• v.3 no.1
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• pp.37-45
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• 1998

A new and efficient inverse design method based on the numerical optimization technique has been developed. The 2-D incompressible Navier-Stokes equations are solved for obtaining the objective functions and coupled with the optimization procedure to perform the inverse design. The steepest descent and the conjugate gradient method have been applied to find the searching direction. The golden section method was applied to compute the design variable intervals. It has been found that the airfoil and the pump impellers are well converged to their targeting shapes.

• Journal of the Korean Operations Research and Management Science Society
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• v.16 no.2
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• pp.118-127
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• 1991

In this paper, criteria and algorithms for the optimal service rate in a closed queueing network have been established. The objective is to minimize total cost. It is shown that system throughput is increasing concave over the service rate of a node and cycle time is increasing convex over the set of service times with a single calss of cubsomers. This enables developing an algorithm using a steepest descent method when the cost function for service rate is convex. The efficiency of the algorithm rests on the fact that the steepest descent direction is readily obtained at each iteration from the MVA algorithm. Several numerical examples are presented. The major application of this research is optimization of facility capacity in a manufacturing system.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10b
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• pp.499-502
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• 1996

In this paper, we propose a fuzzy iterative learning controller(FILC). It can control fully unknown dynamic plants through iterative learning. To design learning controllers based on the steepest descent method, it is one of the difficult problems to identify the change of plant output with respect to the change of control input(.part.e/.part.u). To solve this problem, we propose a method as follows: first, calculate .part.e/.part.u using a similarity measure and information in consecutive time steps, then adjust the fuzzy logic controller(FLC) using the sign of .part.e/.part..u. As learning process is iterated, the value of .part.e/.part.u is reinforced. Proposed FILC has the simple architecture compared with previous other controllers. Computer simulations for an inverted pendulum system were conducted to verify the performance of the proposed FILC.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.25 no.6
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• pp.467-473
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• 2012

A functionally graded material (FGM) spacer, which the distribution of dielectric permittivity inside an insulator changes spatially, can considerably reduce the electric field concentration around a high-voltage electrode and along the gas-insulator interface when compared to a conventional spacer with a uniform permittivity distribution. In this research, we propose the FGM spacer with an elliptical permittivity distribution instead of that with a distribution of dielectric permittivity varying along a radial direction only in order to improve efficiently the insulation capability. The optimal design of the elliptical FGM spacer configuration is performed by using the response surface methodology (RSM) combined with the steepest descent method (SDM).

• Communications of the Korean Mathematical Society
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• v.9 no.2
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• pp.439-448
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• 1994

It is known that the steepest descent(SD) method and the conjugate gradient(CG) method [1, 2, 5, 6] converge when these methods are applied to solve linear systems of the form Ax = b, where A is symmetric and positive definite. For some finite difference discretizations of elliptic problems, one gets positive definite matrices that are almost symmetric. Practically, the SD method and the CG method work for these matrices. However, the convergence of these methods is not guaranteed theoretically. The SD method is also called Orthores(1) in iterative method papers. Elman [4] states that the convergence proof for Orthores($\kappa$), with $\kappa$ a positive integer, is not heard. In this paper, we prove that the SD method and the CG method converge when the $\iota$$^2$ matrix norm of the non-symmetric part of a positive definite matrix is less than some value related to the smallest and the largest eigenvalues of the symmetric part of the given matrix.(omitted)

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2008.04a
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• pp.418-420
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• 2008

얼굴 윤곽선 검출을 위해 그동안 많은 알고리즘이 연구되었다. 그리고 최근에 기존 Active Appearance Model(AAM)에 비해 성능이 개선된 Boosted Appearance Model (BAM)가 Liu에 의해제안되었다. BAM에서는 매 반복 단계마다 Steepest Descent 영상을 구해야 하는데 입력영상의 워핑을 해야 하므로 이것은 계산량이 많다. 본 논문은 BAM을 사용하면서 매번 계산되어야 하는 입력 영상의 워핑을 대신해 템플릿이 워핑함으로써 계산 시간을 줄일 수 있는 방법을 제시한다. 템플릿은 약한 분류기에 사용되는 Haar-like feature들로 이것은 입력 영상에 비해 크기가 매우 작으므로 제안된 방법을 사용하면 Steepest Descent 영상을 구하는데 필요한 워핑 속도를 줄일 수 있다.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.25 no.7A
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• pp.978-985
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• 2000

Blind equalizers recover the transmitted data using statistical characteristics of the signal alone. Among many alternatives, steepest gradient descent type algorithms such as the CMA and Sato algorithm are most widely utilized in practice. In this paper we propose a dual-mode NCMA algorithm, which combines the advantages of the dual mode CMA and Normalized CMA (NCMA) with the dual mode phase recovery algorithm. In addition, we perform computer simulations to demonstrate the performance improvement of the proposed algorithm with a QAM system. Simulation results show that the presented algorithm has a faster convergence speed and smaller steady-state residual error than the CMA and dual-mode CMA.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.62 no.1
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• pp.95-100
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• 2013

This paper presents a new state feedback control approach for communication networks based control systems in which control input and output observation time-delay natures are generally occurred in practice. We first establish a generic state feedback control framework based on well-known linear system theory. A maximum time-delay value which allows critical stability of whole control system are defined to make a positive definite Lyapunov function which is mathematically composed of controlled system states. We analytically derive its control parameters by using a steepest descent optimization method in order to guarantee a stability condition through Lyapunov theory. Computer simulation is numerically carried out for demonstrating reliability of the proposed NCS algorithm and a comparative study is accomplished to prove its superiority for which the traditional control approach for NCS is made use of under same simulation scenarios.

• Proceedings of the Korean Information Science Society Conference
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• 2006.10a
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• pp.39-42
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• 2006

뉴럴네트워크에서 학습은 에러를 줄이는 방법으로 구현 된다. 이 때 parameter 공간에서 Risk function은 multi-minima potential로 표현 될 수 있으며 우리의 목적은 global minimum weight 좌표를 얻는 것이다. 이전의 연구로는 Attouch et al.의 damped oscillator 방정식을 이용한 방법이 있고, Qian의 critically damped oscillator를 통한 steepest descent의 momentum과 learning parameter 유도가 있다. 우리는 이 두 연구를 참고로 manifold 상에서 최단 경로인 geodesic을 Newton 역학의 Lagrangian에 적용함으로써 adaptive steepest descent 학습법을 얻었다. 우리는 이 새로운 방법을 Rosenbrock 과 Griewank 포텐셜들에 적용하여 그 성능을 알아 본다.