• 한국광학회지
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• 제12권2호
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• pp.109-114
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• 2001

광학설계의 최적화에서는 광학수차를 줄이면서 광학계의 제한조건을 유지시켜야하며, 이를 위하여 Lagrange 부정승수법이 사용되고 있다. 이 과정에서 제한조건이 merit function의 error 항보다 우선적으로 보정된다. 본연구에서는 이를 이용하여 merit function에서 절대값이 큰 error의 보정조건을 제한조건으로 변경하여 우선적으로 보정하는 최적화의 능동적 제어법을 제안하고 이를 사진렌즈계의 최적화에 적용하였다.

• Computers and Concrete
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• 제18권5호
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• pp.983-998
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• 2016

Structural optimization is one of the most important topics in structural engineering and has a wide range of applicability. Therefore, the main objective of the present study is to apply the Lagrange Multiplier Method (LMM) for minimum cost design of singly and doubly reinforced rectangular concrete beams. Concrete and steel material costs are used as objective cost function to be minimized in this study, and ultimate flexural strength of the beam is considered to be as the main constraint. The ultimate limit state method with partial material strength factors and equivalent concrete stress block is used to derive general relations for flexural strength of RC beam and empirical coefficients are taken from topic 9 of the Iranian National Building Regulation (INBR9). Optimum designs are obtained by using the LMM and are presented in closed form solutions. Graphical representation of solutions are presented and it is shown that proposed design curves can be used for minimum cost design of the beams without prior knowledge of optimization and without the need for iterative trials. The applicability of the proposed relations and curves are demonstrated through two real life examples of SRB and DRB design situations and it is shown that the minimum cost design is actually reached using proposed method.

• 한국구조물진단유지관리공학회 논문집
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• 제1권1호
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• pp.113-124
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• 1997

Based on the recent developments of the reliability-based structural analysis and design as well as the extending knowledge on the probabilistic characteristics of load and resistances, the probability based design criteria have been successfully developed for many standards. Since the probabilistic characteristics depend highly on the local load and resistances, it is recognized to develop the design criterion compatible with domestic requirements. The existing optimum design methods, which are generally based on the structural theory and certain engineering exprience, do not realistically consider the uncertainties of load and resistances and the basic reliability concepts. This study is directed to propose a optimum design based Expected Total Cost Minimization on two-way slab system which could possibly replace optimum design based traditional provisions of the current code, based on the AFOSM reliablity theory.

• 한국공간구조학회:학술대회논문집
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• 한국공간구조학회 2006년도 춘계 학술발표회 논문집 제3권1호(통권3호)
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• pp.165-169
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• 2006

This study presents a new stress analysis method to be substituted for the elastic analysis in such a plastic design procedure. This method is accompanied by an efficient mathematical tool which can be easily handled by personal computer. The method also easily accepts arbitrary strategies by the designer for selection member size.

• 한국콘텐츠학회논문지
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• 제9권4호
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• pp.27-33
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• 2009

비디오 부호화에서의 라그랑지안 계수의 선정은 Rate-Distortion Optimization의 성능을 결정하는 중요한 요소이다. H.264의 참조소프트웨어인 JM에서는 모든 매크로블록에 하나의 RDO모델을 사용한다. 그러나 각각의 매크로블록의 특성은 다르기 때문에 그에 맞는 RDO모델을 적용함으로써 성능향상을 기대할 수 있다. 본 논문에서는 매크로블록의 특성에 따라서 적응적인 RDO알고리즘을 제안한다. 우리는 실험적으로 각 매크로블록의 특성에 따른 최적의 라그랑지안 계수를 얻었다. 성능평가를 위하여 제안한 알고리즘은 참조 소프트웨어 JM10.2에 적용되었고, 실험결과 약 0.2dB정도의 화질 향상을 얻을 수 있었다.

• 전기의세계
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• 제14권3호
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• pp.10-17
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• 1965

This paper presents a method of the voltage-reactive power control in the long and short range operations and introduces a conception, "optimum control pattern." The optimum control pattern, aiming at the over-all system control, is defined as the optimum voltage distribution which minimizes the system operating cost under the conditions that the specified power be supplied and the system voltage be kept within the specified bounds. The following procedure was adopted to obtain this optimum pattern. In the first place, a power system was divided into three blocks, namely, load, substation and generator. Lagrange's, multiplier method is applied to each block in turn, paying attention only at the operating voltage distribution. Phase angles at each bus are then modified so that the continuity of active power is maintained. This procedure may be called "block relaxation method with Lagrange's multipliers." In a long range operation, this control pattern determines the optimum installation capacity of reactive power sources. In a short range operation, it also gives the reference state of real time control and the optimum switching capacity of reactive power souces. The real time control problem is also studied from the standpoint of cooperation of control devices such as generators, shunt capacitors, shunt reactors and ratio load controllers. A proposal for the real time control will contribute to the automation of power system operation in the near future. in the near future.

• Industrial Engineering and Management Systems
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• 제9권1호
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• pp.10-19
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• 2010

This paper presents an extended computing procedure for the global optimization of the triple response system (TRS) where the response functions are nonconvex (nonconcave) quadratics and the input factors satisfy a radial region of interest. The TRS arising from response surface modeling can be approximated using a nonlinear mathematical program involving one primary (objective) function and two secondary (constraints) functions. An optimization algorithm named triple response surface algorithm (TRSALG) is proposed to determine the global optimum for the nondegenerate TRS. In TRSALG, the Lagrange multipliers of target (secondary) functions are computed by using the Hooke-Jeeves search method, and the Lagrange multiplier of the radial constraint is located by using the trust region (TR) method at the same time. To ensure global optimality that can be attained by TRSALG, included is the means for detecting the degenerate case. In the field of numerical optimization, as the family of TR approach always exhibits excellent mathematical properties during optimization steps, thus the proposed algorithm can guarantee the global optimal solution where the optimality conditions are satisfied for the nondegenerate TRS. The computing procedure is illustrated in terms of examples found in the quality literature where the comparison results with a gradient-based method are used to calibrate TRSALG.

• 한국전산유체공학회지
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• 제19권3호
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• pp.85-90
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• 2014

The purpose of this study is to develop a new Meshless Method to solve 2-D compressible flow problems numerically. This paper includes a revised Least Square method that improves robustness compared with its original version by removing excessive numerical oscillation which occurs when points are randomly distributed. Numerical analyses of hypersonic flow over a blunt body were carried out using the method, then robustness, accuracy and convergence of their results were compared with those obtained from the original method.

• Journal of Mechanical Science and Technology
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• 제17권4호
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• pp.538-544
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• 2003

Although many methodologies exist for determining the constrained equations of motion, most of these methods depend on numerical approaches such as the Lagrange multiplier's method expressed in differential/algebraic systems. In 1992, Udwadia and Kalaba proposed explicit equations of motion for constrained systems based on Gauss's principle and elementary linear algebra without any multipliers or complicated intermediate processes. The generalized inverse method was the first work to present explicit equations of motion for constrained systems. However, numerical integration results of the equation of motion gradually veer away from the constraint equations with time. Thus, an objective of this study is to provide a numerical integration scheme, which modifies the generalized inverse method to reduce the errors. The modified equations of motion for constrained systems include the position constraints of index 3 systems and their first derivatives with respect to time in addition to their second derivatives with respect to time. The effectiveness of the proposed method is illustrated by numerical examples.

• Communications for Statistical Applications and Methods
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• 제4권3호
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• pp.663-676
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• 1997

We obtain the simultaneous unit roots test statistics for both regular and seasonal unit roots in a time series with possible seasonal deterministic trends. The limiting distributions of the proposed test statistics are derived and empirical percentiles of the test statistics are tabulated for some seasonal periods. The power and size of the test statistics are examined for finite samples through a Monte Carlo simulation and Compared with those of the Lagrange multiplier test.