• Journal of the Computational Structural Engineering Institute of Korea
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• v.25 no.6
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• pp.469-476
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• 2012

In this paper, a finite element domain decomposition method using local and mixed Lagrange multipliers for a large scal structural analysis is presented. The proposed algorithms use local and mixed Lagrange multipliers to improve computational efficiency. In the original FETI method, classical Lagrange multiplier technique was used. In the dual-primal FETI method, the interface nodes are used at the corner nodes of each sub-domain. On the other hand, the proposed FETI-local analysis adopts localized Lagrange multipliers and the proposed FETI-mixed analysis uses both global and local Lagrange multipliers. The numerical analysis results by the proposed algorithms are compared with those obtained by dual-primal FETI method.

• Journal of the Korean Mathematical Society
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• v.60 no.2
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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.

• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.2
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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.

• Journal of Ocean Engineering and Technology
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• v.10 no.3
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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.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.10
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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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• v.1 no.1
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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.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 2014.11a
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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.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.29 no.12 s.243
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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.

• Transactions of Materials Processing
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• v.11 no.4
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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.

• Journal of Korea Multimedia Society
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• v.5 no.3
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• pp.249-254
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• 2002

We consider a buffer-constrained adaptive quantization algorithm for image compression. Buffer control algorithm was considered with source coding scheme by some researchers and recently a formal description of the algorithm in terms of rate-distortion has been developed. We propose a buffer control algorithm that incorporates the buffer occupancy into the Lagrange multiplier form in a rate-distortion cost measure. Although the proposed algorithm provides the suboptimal performance as opposed to the optimal Vieterbi algorithm, it can be implemented with very low computaional complexity. In addition stability of this buffer control algorithm has been mentioned briefly using Liapnov stability theory.