• 대한수학회지
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• 제52권6호
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• pp.1195-1207
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• 2015

Lagrange multiplier method for solving the contact problem in elasticity is considered. Based on lower semicontinuity of sensitivity functional we prove the convergence of modified dual scheme to corresponding saddle point.

• 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.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제14권11호
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• pp.4595-4610
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• 2020

In the practical communication environment, the accurate channel state information (CSI) is difficult to obtain, which will cause the mismatch of resource and degrade the system performance. In this paper, to account for the channel uncertainties, a robust power allocation scheme for a downlink Non-orthogonal multiple access (NOMA) heterogeneous network (HetNet) is designed to maximize energy efficiency (EE), which can ensure the quality of service (QoS) of users. We conduct the robust optimization model based on worse-case method, in which the channel gains belong to certain ellipsoid sets. To solve the non-convex non-liner optimization, we transform the optimization problem via Dinkelbach method and sequential convex programming, and the power allocation of small cell users (SCUs) is achieved by Lagrange dual approach. Finally, we analysis the convergence performance of proposed scheme. The simulation results demonstrate that the proposed algorithm can improve total EE of SCUs, and has a fast convergence performance.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제19권2호
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• pp.179-192
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• 2012

We find the solution minimizing the shortfall risk by using the Lagrange-multiplier method. The conventional duality method in the expected utility maximization problem is used and we get the same results as in the paper [21].

• 대한수학회지
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• 제54권2호
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• pp.461-477
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• 2017

A dual substructuring method with a penalty term was introduced in the previous works by the authors, which is a variant of the FETI-DP method. The proposed method imposes the continuity not only by using Lagrange multipliers but also by adding a penalty term which consists of a positive penalty parameter ${\eta}$ and a measure of the jump across the interface. Due to the penalty term, the proposed iterative method has a better convergence property than the standard FETI-DP method in the sense that the condition number of the resulting dual problem is bounded by a constant independent of the subdomain size and the mesh size. In this paper, a further study for a dual iterative substructuring method with a penalty term is discussed in terms of its convergence analysis. We provide an improved estimate of the condition number which shows the relationship between the condition number and ${\eta}$ as well as a close spectral connection of the proposed method with the FETI-DP method. As a result, a choice of a moderately small penalty parameter is guaranteed.

• Communications for Statistical Applications and Methods
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• 제21권5호
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• pp.395-409
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• 2014

Data limited, partial, or incomplete are known as an ill-posed problem. If the data with ill-posed problems are analyzed by traditional statistical methods, the results obviously are not reliable and lead to erroneous interpretations. To overcome these problems, we propose a dual generalized maximum entropy (dual GME) estimator for panel data regression models based on an unconstrained dual Lagrange multiplier method. Monte Carlo simulations for panel data regression models with exogeneity, endogeneity, or/and collinearity show that the dual GME estimator outperforms several other estimators such as using least squares and instruments even in small samples. We believe that our dual GME procedure developed for the panel data regression framework will be useful to analyze ill-posed and endogenous data sets.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제18권1호
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• pp.17-26
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• 2014

This paper presents development of an improved domain decomposition method for large scale structural problem that aims to provide high computational efficiency. In the previous researches, we developed the domain decomposition algorithm based on augmented Lagrangian formulation and proved numerical efficiency under both serial and parallel computing environment. In this paper, new computational analysis by the proposed domain decomposition method is performed. For this purpose, reduction in computational time achieved by the proposed algorithm is compared with that obtained by the dual-primal FETI method under serial computing condition. It is found that the proposed methods significantly accelerate the computational speed for a linear structural problem.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제12권5호
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• pp.2063-2081
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• 2018

A resource allocation algorithm is proposed in this paper to simultaneously minimize the total system power consumption and maximize the system throughput for the downlink of multi-user multiple input multiple output-orthogonal frequency division multiplexing (MIMO-OFDM) systems. With the Lagrange dual decomposition method, we transform the original problem to its convex dual problem and prove that the duality gap between the two problems is zero, which means the optimal solution of the original problem can be obtained by solving its dual problem. Then, we use convex optimization method to solve the dual problem and utilize bisection method to obtain the optimal dual variable. The numerical results show that the proposed algorithm is superior to traditional single-objective optimization method in both the system throughput and the system energy consumption.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2000년도 추계학술대회 논문집
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• pp.670-673
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• 2000

This paper attempt analysis and computer simulation of dynamics of a set of dual multi-joint fingers with soft-deformable tips which are grasping. Firstly, a set of differential equation describing dynamics of the fingers and object together with geometric constraint of tight area-contacts is formulated by Euler-Lagrange's formalism. Secondly, problems of controlling both the internal force and the rotation angle of the grasped object under the constraints of area-contacts of tight area-contacts are discussed. The effect of geometric constraints of area-contacts on motion of the overall system is analyzed and a method of computer simulation for overall system of differential-algebraic equations is presented. Finally, simulation results are shown and the effects of geometric constraints of area-contact is discussed.

• 한국위성정보통신학회논문지
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• 제12권2호
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• pp.51-55
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• 2017

본 논문에서는 RF 에너지 하비스팅 네트워크에서 최대 전송 파워량 제한 및 최소 채널 용량 달성에 관한 제약조건을 만족시키며 에너지 하비스팅율과 채널 용량을 최대화 시키는 연구를 진행하였다. 전력 분할 기법 (power-splitting scheme) 기반 안테나로 구성된 주파수 분할 다중접속 환경에서 하나의 액세스 포인트 (access point)로부터 무선 에너지와 정보를 사용자들에게 동시에 송수신하는 모델을 가정하였다. 네트워크 성능 지표로서 에너지 효율 (energy efficiency)을 정의하고 이를 최대화 시킬 수 있는 Lagrange 이중 분해 기반의 최적화 솔루션을 제안하였다. 모의실험 결과를 통해 제안한 솔루션이 설정된 제한조건들을 만족하면서 효과적으로 에너지 효율을 최대화시키는 것을 확인하였다.