• 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.

• 대한수학회지
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• 제60권2호
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• pp.375-393
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• 2023

Rabinowitz action functional is the Lagrange multiplier functional of the negative area functional to a constraint given by the mean value of a Hamiltonian. In this note we show that on a symplectization there is a one-to-one correspondence between gradient flow lines of Rabinowitz action functional and gradient flow lines of the restriction of the negative area functional to the constraint. In the appendix we explain the motivation behind this result. Namely that the restricted functional satisfies Chas-Sullivan additivity for concatenation of loops which the Rabinowitz action functional does in general not do.

• 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.

• 한국해양공학회지
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• 제10권3호
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• pp.96-104
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• 1996

Hamilton's principle is used to derive Euler-Lagrange equations for free surface flow problems of incompressible ideal fluid. The velocity field is chosen to satisfy the continuity equation a priori. This approach results in a hierarchial set of governing equations consist of two evolution equations with respect to two canonical variables and corresponding boundary value problems. The free surface elevation and the Lagrange's multiplier are the canonical variables in Hamilton's sense. This Lagrange's multiplier is a velocity potential defined on the free surface. Energy is conserved as a consequence of the Hamiltonian structure. These equations can be applied to waves in water of finite depth including generalization of Hamilton's equations given by Miles and Salmon.

• 대한기계학회논문집
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• 제17권10호
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• pp.2457-2466
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• 1993

A simple method is presented for determining transient responses of locally nonlinear structures using substructure eigenproperties and Lagrange multiplier technique. Although the method is based upon the mode synthesis formulation procedure, the equations of the combined whole structure are not constructed compared with the conventional methods. Lagrange multi-pliers are used to enforce the conditions of geometric compatibility between the substructure interfaces and they are treated as external forces on each substructure itself. Substructure eigenvalue problem is defined with the substructure interface free of fixed. The transient analysis is based upon the recurrence discrete-time state equations and offers the simplicity of the Euler integration method without requiring small time increment and iterative solution procedure. Numerical examples reveal that the method is very accurated and efficient in calculating transient responses compared with the direct numerical integration method.

• 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.

• 한국방송∙미디어공학회:학술대회논문집
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• 한국방송공학회 2014년도 추계학술대회
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• pp.197-199
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• 2014

현재 MPEG에서 표준화 중인 IVC(Internet Video Coding)에서는 기존의 비디오 부호화 표준과 같이 Lagrange 계수 기반의 율-왜곡 최적화(RDO: Rate-Distortion Optimization)를 사용하여 최적의 부호화 모드를 결정하고 있다. RDO를 위하여 픽쳐 타입과 부호화 구조에 따라 미리 결정된 Lagrange 계수가 선택적으로 사용되고 있다. 한편 IVC에서는 저지연 모드 부호화 구조에서 비참조 P 프레임 부호화 기법을 선택적으로 사용하여 상당한 부호화 성능을 얻고 있다. 하지만 Lagrange 계수 선택에서 기존의 P 프레임과는 다른 비참조 P 프레임의 RD 특성이 반영되고 있지 않다. 본 논문에서는 비참조 P 프레임의 RD 특성을 고려하여 기존의 기법을 확장한 새로운 Lagrange 계수 선택 기법을 제안한다. 실험결과 제안기법은 IVC 시험모델 ITM 10.0에서 기존 기법 대비 0.4%의 비트율 감소를 얻을 수 있음을 확인하였다.

• 대한기계학회논문집A
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• 제29권12권
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• pp.1629-1637
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• 2005

Optimum sensitivity analysis (OSA) is the process to find the sensitivity of optimum solution with respect to the parameter in the optimization problem. The prevalent OSA methods calculate the optimum sensitivity as a post-processing. In this research, a simple technique is proposed to obtain optimum sensitivity as a result of the original optimization problem, provided that the optimum sensitivity of objective function is required. The parameters are considered as additional design variables in the original optimization problem. And then, it is endowed with equality constraints to penalize the additional variables. When the optimization problem is solved, the optimum sensitivity of objective function is simultaneously obtained as Lagrange multiplier. Several mathematical and engineering examples are solved to show the applicability and efficiency of the method compared to other OSA ones.

• 소성∙가공
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• 제11권4호
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• pp.355-362
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• 2002

In this study, an axi-symmetric finite element program for elastic analysis of the die set shrink fitted in cold extrusion was developed. The geometrical constraint according to shrink fit was enforced by employing the Lagrange multiplier method. The numerical results for strain and stress distributions in the die set including single and multi stress rings assembled by shrink fit were compared well with the Lame's equation for thick-walled solution available in the literature. To extend the applicability of the analysis program developed, various cases without or with stress ring and with pre-stress applied on stress ring were numerically investigated as well. This numerical approach enables the optimization study to determine optimal dimensions of die set to improve tool life for practical use in industry.

• 한국멀티미디어학회논문지
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• 제5권3호
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• pp.249-254
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• 2002

본 논문에서는 영상압축을 위한 버퍼제약에 의한 적응양자화 알고리즘에 대해서 논하고져 한다. 버퍼제약에 의한 알고리즘은 source coding과 더불어 그간 연구되다가, 최근에는 비트율 왜곡의 이름으로 연구가 더욱 진전돼 오고 있다. 여기에서 우리는 버퍼 occupancy의 값이 비트율 왜곡의 측정치에서 Lagrange multiplier 형식으로 통합되는 것을 제안한다. 여기서 제안하는 알고리즘이 Viterbi 알고리즘과는 반대로 최적치에는 약간 못미치는 성능을 보여주지만, 대신 계산의 복잡도가 매우 낮을 뿐 아니라, 버퍼 제어 알고리즘의 안정도를 Liapnov의 안정화이론을 이용해서 간단하게 설명 할 수 있다는 것이다.