• Journal of Korean Society of Industrial and Systems Engineering
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• v.37 no.1
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• pp.50-59
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• 2014

In this paper, we develop an efficient approach to solve a multiple-item budget-constraint newsboy problem with a reservation policy. A conventional approach for solving such problem utilizes an approximation for the evaluation of an inverse of a Gaussian cumulative density function when the argument of the function is small, and a heuristic method for finding an optimal Lagrangian multiplier. In contrast to the conventional approach, this paper proposes more accurate method of evaluating the function by using the normalization and an effective numerical integration method. We also propose an efficient way to find an optimal Lagrangian multiplier by proving that the equation for the budget-constraint is in fact a monotonically increasing function in the Lagrangian multiplier. Numerical examples are tested to show the performance of the proposed approach with emphases on the behaviors of the inverse of a Gaussian cumulative density function and the Lagrangian multiplier. By using sensitivity analysis of different budget constraints, we show that the reservation policy indeed provides greater expected profit than the classical model of not having the reservation policy.

• Journal of the Korean Data and Information Science Society
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• v.17 no.3
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• pp.919-925
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• 2006

Maximum likelihood estimate(MLE) is obtained from the partial log-likelihood function for the cell probabilities of two way incomplete contingency tables proposed by Chen and Fienberg(1974). The partial log-likelihood function is modified by adding lagrangian multiplier that constraints can be incorporated with. Variances of MLE estimators of population proportions are derived from the matrix of second derivatives of the loglikelihood with respect to cell probabilities. Simulation results, when data are missing at random, reveal that Complete-case(CC) analysis produces biased estimates of joint probabilities under MAR and less efficient than either MLE or MI. MLE and MI provides consistent results under either the MAR situation. MLE provides more efficient estimates of population proportions than either multiple imputation(MI) based on data augmentation or complete case analysis. The standard errors of MLE from the proposed method using lagrangian multiplier are valid and have less variation than the standard errors from MI and CC.

• Journal of Mechanical Science and Technology
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• v.14 no.10
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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.

• Korea-Australia Rheology Journal
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• v.19 no.4
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• pp.233-242
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• 2007

We performed a numerical investigation to find out the optimal choice of the spatial discretization in the distributed-Lagrangian-multiplier/fictitious-domain (DLM/FD) method for the solid/fluid interaction problem. The elastic solid bar attached on the bottom in a pressure-driven channel flow of a Newtonian fluid was selected as a model problem. Our formulation is based on the scheme of Yu (2005) for the interaction between flexible bodies and fluid. A fixed regular rectangular discretization was applied for the description of solid and fluid domain by using the fictitious domain concept. The hydrodynamic interaction between solid and fluid was treated implicitly by the distributed Lagrangian multiplier method. Considering a simplified problem of the Stokes flow and the linearized elasticity, two numerical factors were investigated to clarify their effects and to find the optimum condition: the distribution of Lagrangian multipliers and the solid/fluid interfacial condition. The robustness of this method was verified through the mesh convergence and a pseudo-time step test. We found that the fluid stress in a fictitious solid domain can be neglected and that the Lagrangian multipliers are better to be applied on the entire solid domain. These results will be used to extend our study to systems of elastic particle in the Stokes flow, and of particles in the viscoelastic fluid.

• Steel and Composite Structures
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• v.29 no.2
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• pp.243-256
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• 2018

This study conducts an optimization and sensitivity analysis on rectangular reinforced concrete (RC) beam using Lagrangian Multiplier Method (LMM) as programming optimization computer soft ware. The analysis is conducted to obtain the minimum design cost for both singly and doubly RC beams according to the specifications of three regulations of American concrete institute (ACI), British regulation (BS), and Iranian concrete regulation (ICS). Moreover, a sensitivity analysis on cost is performed with respect to the effective parameters such as length, width, and depth of beam, and area of reinforcement. Accordingly, various curves are developed to be feasibly utilized in design of RC beams. Numerical examples are also represented to better illustrate the design steps. The results indicate that instead of complex optimization relationships, the LMM can be used to minimize the cost of singly and doubly reinforced beams with different boundary conditions. The results of the sensitivity analysis on LMM indicate that each regulation can provide the most optimal values at specific situations. Therefore, using the graphs proposed for different design conditions can effectively help the designer (without necessity of primary optimization knowledge) choose the best regulation and values of design parameters.

• Journal of Korean Society of Steel Construction
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• v.10 no.3 s.36
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• pp.393-406
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• 1998

In this study buckling behavior of orthotropic plate with a longitudinal stiffener under in-plane linearly distributed loads is investigated. All edges of plate are assumed to be simply supported and the stiffener is considered as a beam element. For the equation of buckling analysis Rayleigh-Ritz method is employed. The upper limit of the critical stress at various location of stiffener is determined by using Lagrangian multiplier method. Buckling analysis is performed for the various position of stiffener and for the various width ratios between plate and stiffener. The parametric study shows that, when four edges of plate are simply supported, the most effective position for a longitudinal stiffener is at the location of which the upper limit of the stress is the maximum.

• The Journal of the Korea Contents Association
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• v.9 no.4
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• pp.27-33
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• 2009

Selection of the Lagrangian multiplier is a key factor to determine the performance of Rate-Distortion Optimization (RDO) in video coding. JM, reference S/W of H.264, employs only one RDO model for all macroblock. However, since the characteristics of macroblocks are different, RDO model adaptive to their characteristics can give some performance improvement. In this paper, we propose an RDO algorithm adaptive to characteristics of macroblocks. We empirically obtain the optimal Lagrangian multipliers considering characteristics of macroblocks. For performance evaluation, the proposed method is applied to JM10.2 and, as a result, we have PSNR gain of 0.2dB on average.

• The Korean Journal of Applied Statistics
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• v.28 no.2
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• pp.189-200
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• 2015

Stationary bootstrapping is applied to a Lagrangian multiplier (LM) test to test market microstructure noise (MMN) in financial asset prices. A Monte-Carlo experiment shows that the bootstrapping method improves the size of the original LM test which has some size distortion for conditional heteroscedastic models. The proposed test is illustrated for real data sets like KOSPI index and Won-Dollar exchange rate.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2001.10a
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• pp.17-20
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• 2001

This paper presents the results of an elastic buckling analysis of elastically restrained orthotropic plate with a longitudinal stiffener under in-plane linearly distributed load. It is assumed that the loaded edges of web plate are simply supported and other two edges are elastically restrained against rotation. The stiffener is modeled as a beam element and its torsional rigidity is neglected. For the buckling analysis Lagrangian multiplier method is employed. The effects of restraint and longitudinal stiffener are presented in a graphical form.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.58 no.1
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• pp.23-27
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• 2009

The joint dispatch of regional electricity markets can improve the overall economic efficiency of interconnected markets by increasing the combined social welfare of the interconnected markets. This paper presents a new decentralized optimization technique based on Augmented Lagrangian Relaxation (ALR) to perform the joint dispatch of interconnected electricity markets. The Block Coordinate Descent (BCD) technique is applied to decompose the inseparable quadratic term of the augmented Lagrangian equation into individual market optimization problems. The Interior Point/Cutting Plane (IP/CP) method is used to update the Lagrangian multiplier in the decomposed market optimization problem. The numerical example is presented to validate the effectiveness of the proposed decentralized method.