• Journal of Mechanical Science and Technology
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• 제14권10호
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• pp.1122-1130
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• 2000

Based on the value of the Lagrange multiplier and the degree of constraint activeness, a new update rule is proposed for penalty parameters of the ALM method. The theoretical exposition of this suggested update rule is presented by using the algorithmic interpretation and the geometric interpretation of the augmented Lagrangian. This interpretation shows that the penalty parameters can effect the performance of the ALM method. Also, it offers a lower limit on the penalty parameters that makes the augmented Lagrangian to be bounded. This lower limit forms the backbone of the proposed update rule. To investigate the numerical performance of the update rule, it is embedded in our ALM based dynamic response optimizer, and the optimizer is applied to solve six typical dynamic response optimization problems. Our optimization results are compared with those obtained by employing three conventional update rules used in the literature, which shows that the suggested update rule is more efficient and more stable than the conventional ones.

• 대한기계학회논문집
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• 제15권2호
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• pp.544-556
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• 1991

The optimization of many engineering design problems requires a nonlinear programming algorithm that is robust and efficient. A general-purpose nonlinear optimization program IDOL (Interactive Design Optimization Library) is developed based on the Augmented Lagrange Mulitiplier (ALM) method. The ideas of selecting a good initial design point, using resonable initial values for Lagrange multipliers, constraints scaling, descent vector restarting, and dynamic stopping criterion are employed for computational enhancement to the ALM method. A descent vector is determined by using the Broydon-Fletcher-Goldfarb-Shanno (BFGS) method. For line search, the Incremental-Search method is first used to find bounds on the solution, then the bounds are reduced by the Golden Section method, and finally a cubic polynomial approximation technique is applied to locate the next design point. Seven typical test problems are solved to show IDOL efficient and robust.

• Industrial Engineering and Management Systems
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• 제1권1호
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• pp.29-45
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• 2002

In this study, we consider infinite supply of raw materials and backlogged demands as given two boundary conditions. And we need not make any specific assumptions about the inter-arrival of external demand and service time distributions. We propose a numeric model and an algorithm in order to compute the first two moments of inter-departure process. Entropy enables us to examine the convergence of this process and to derive measurable relations of this process. Also, lower bound on the variance of inter-departure process plays an important role in proving the existence and uniqueness of an optimal solution for a numeric model and deriving the convergence order of augmented Lagrange multipliers method applied to a numeric model. Through these works, we confirm some structural properties and numeric examples how the validity and applicability of our study.

• 한국전산구조공학회논문집
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• 제25권6호
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• pp.469-476
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• 2012

본 논문에서는 대규모 구조해석을 위하여 국부(local) 및 전역-국부 혼합(mixed) Lagrange 승수(Lagrange multiplier)를 이용한 새로운 유한요소 영역분할 기법을 제시한다. 제시되는 FETI 알고리즘은 계산 효율성을 향상시키기 위하여 기존의 FETI 기법들에서 사용되어 온 전통적인 Lagrange 승수법과는 달리, 국부 및 전역-국부 혼합 Lagrange 승수를 도입하고 ALF(Augmented Lagrangian Formulation)과의 결합을 유도하여 공유면 문제(interface problem)의 해의 수렴성을 향상 시켰다. 추가적으로, 몇 가지 수치예제 계산을 통해 기존의 FETI-DP 기법과 비교하여 유연도 행렬의 조건수, 계산 시간 그리고 메모리 사용량에 대한 계산결과를 제시하였다.

• 오토저널
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• 제11권2호
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• pp.24-33
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• 1989

본 고에서는 이러한 추세에 따라서, 보다 효율적인 optimization program에 대해서 소개하고자 한다. 사용한 최적화 알고리즘은 ALM(augmented lagrange multiplier) 방법을 적용해서 구속조건이 있는 문제를 구속조건이 없는 문제로 변환한 후, self-scaling BFGS(broydon-flecher-goldfarb-schanno)를 적용한다. BFGS의 각 descent 방향에서의 step 길이는, sequential search로 unimodal point를 구해서, golden section 방법으로 refine을 한후, cubic approximation을 적용해서 구한다.

• 대한기계학회논문집A
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• 제22권4호
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• pp.811-825
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• 1998

An approximate line search is presented for dynamic response optimization with Augmented Lagrange Multiplier(ALM) method. This study empolys the approximate a augmented Lagrangian, which can improve the efficiency of the ALM method, while maintaining the global convergence of the ALM method. Although the approximate augmented Lagragian is composed of only the linearized cost and constraint functions, the quality of this approximation should be good since an approximate penalty term is found to have almost second-order accuracy near the optimum. Typical unconstrained optimization algorithms such as quasi-Newton and conjugate gradient methods are directly used to find exact search directions and a golden section method followed by a cubic polynomial approximation is empolyed for approximate line search since the approximate augmented Lagrangian is a nonlinear function of design variable vector. The numberical performance of the proposed approach is investigated by solving three typical dynamic response optimization problems and comparing the results with those in the literature. This comparison shows that the suggested approach is robust and efficient.

• 대한기계학회논문집
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• 제12권1호
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• pp.106-115
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• 1988

본 연구에서는 경계층 유동을 충류, 천이, 난류 영역을 포함하는 압축성 유동으로 가정하였고, Morgan 등이 제시한 새로운 질점분할 방법을 사용하여 속도분포를 계산하고, 점성 압축성 효과를 고려하기 위하여 viscous--inviscid interaction 법을 사용하였고 이 계산 결과를 기존의 실험값과 비교하여,타당성을 확인하였다.그리고 최적 양력의 익형 설계는 Augmented Lagrange multiplier 법을 사용하였고 비구속 조건을 갖는 목적함수 augmented lagrangian의 최소화는 Davidan-Fletcher-Powell 방법 중 self-scaling quasi-Newton algorithm을 사용하였다. 그리고 NACA 23012를 기본 익형으로 하고 NACA 64-2-415, NACA 64-2-A215, NACA 65-3-218를 보상 익형으로 하여 최대 양력익형을 설계 하였다.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 1997년도 춘계학술대회 논문집
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• pp.312-317
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• 1997

This paper present an optimum design for the rotor-bearing system of a high-speed (80000RPM) ultra-centrifuge supported by ball bearings with nonlinear stiffness characteristics. To obtain the nonlinear bearing stiffnesses, a ball bearing is modelled in five degrees of freedom and is analyzed quasi-statically. The dynamic behaviors of the nonlinear rotor-bearing system are analyed by using a transfer-matrix method iteratively. For optimum design, minimizing the weight of a rotor is used as a cost function and the Augmented Lagrange Multiplier (ALM) method is employed. The result shows that the rotor-bearing system is optimized to obtain 8% weight reduction.

• 전자공학회논문지A
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• 제31A권3호
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• pp.68-76
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• 1994

In the automatic transistor sizing with computer for optimizing delay and the chip area of CMOS digital circuits, conventionally either a mathematical method or a heuristic method has been used. In this paper, we present a new method of transistor sizing, a sort of combination of the above two methods, in which the mathematical method is used for sizing of critical paths and the heuristic method is used for desizing of non-critical paths. In order to reduce the overall problem dimension, a basic block called an extended stage is introduced which includes a basic stage, parallel transistors and complementary part. Optimization for multiple critical paths is formulated as a problem of area minimization subject to delay constraints and is solved by the augmented Lagrange multiplier method. The transistor sizes along non-critical paths are decreased successively without affecting the critical path delay times. The proposed scheme was successfully applied to several test circuits.

• Tribology and Lubricants
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• 제8권2호
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• pp.26-34
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• 1992

This paper suggests a method to predict the flying state of the head slider in a hard disk drive (HDD) by using an optimization technique. The modified Reynolds equation for the hydrodynamic lubrication theory under the slip flow condition is used to describe the air-bearing system and a Finite Volume Method (FVM) is applied to solve the equation. Especially, Augmented Lagrange Multiplier (ALM) method is employed to find the minimum flying height, the pitch angle and the roll angle of the slider, which is shown to be faster and more general than the conventional update schemes. By using the proposed method, the variations of the flying state are analyzed as a function of the slider position in the direction of the disk radius for various disk velocities and skew angles.