• 대한수학회지
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• 제61권2호
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• pp.395-408
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• 2024

There have been numerous studies on the characteristics of the solutions of ordinary differential equations for optimization methods, including gradient descent methods and alternating direction methods of multipliers. To investigate computer simulation of ODE solutions, we need to trace pseudo-orbits by real orbits and it is called shadowing property in dynamics. In this paper, we demonstrate that the flow induced by the alternating direction methods of multipliers (ADMM) for a C² strongly convex objective function has the eventual shadowing property. For the converse, we partially answer that convexity with the eventual shadowing property guarantees a unique minimizer. In contrast, we show that the flow generated by a second-order ODE, which is related to the accelerated version of ADMM, does not have the eventual shadowing property.

• Journal of Electrical Engineering and Technology
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• 제13권5호
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• pp.1778-1790
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• 2018

Based on the requirements and characteristics of multi-zone autonomous decision-making in modern power system, fully distributed computing methods are needed to optimize the economic dispatch (ED) problem coordination of multi-regional power system on the basis of constructing decomposition and interaction mechanism. In this paper, four fully distributed methods based on alternating direction method of multipliers (ADMM) are used for solving the ED problem in distributed manner. By duplicating variables, the 2-block classical ADMM can be directly used to solve ED problem fully distributed. The second method is employing ADMM to solve the dual problem of ED in fully distributed manner. N-block methods based on ADMM including Alternating Direction Method with Gaussian back substitution (ADM_G) and Exchange ADMM (E_ADMM) are employed also. These two methods all can solve ED problem in distributed manner. However, the former one cannot be carried out in parallel. In this paper, four fully distributed methods solve the ED problem in distributed collaborative manner. And we also discussed the difference of four algorithms from the aspects of algorithm convergence, calculation speed and parameter change. Some simulation results are reported to test the performance of these distributed algorithms in serial and parallel.

• 전기학회논문지
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• 제66권7호
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• pp.1078-1082
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• 2017

This paper presents an L1 optimization based filtering technique which effectively eliminates the optical misalignment effects encountered in the squint guidance mode with strapdown seekers. We formulated a series of L1 optimization problems in order to separate the bias and the gradient components from the measured data, and solved them via the alternating direction method of multipliers (ADMM) and sparse matrix decomposition techniques. The proposed technique was able to rapidly detect arbitrary discontinuities and gradient changes from the measured signals, and was shown to effectively cancel the undesirable effects coming from the seeker misalignment angles. The technique was implemented on embedded flight computers and the real-time operational performance was verified via the hardware-in-the-loop simulation (HILS) tests in parallel with the automatic target recognition algorithms and the intra-red synthetic target images.

• Journal of the Korean Data and Information Science Society
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• 제28권6호
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• pp.1229-1244
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• 2017

최근 여러 분야에서 데이터에 근거한 분석방법론에 대한 수요가 증대됨에 따라 이를 처리할 수 있는 최적화 방법이 발전되고 있다. 특히 통계학과 기계학습 분야의 문제들에서 요구되는 다양한 제약 조건은 볼록 최적화 (convex optimization) 방법으로 해결할 수 있다. 본 논문에서 리뷰하는 alternating direction method of multipliers (ADMM) 알고리즘은 선형 제약 조건을 효과적으로 처리할 수 있으며, 합의 방식을 통해 병렬연산을 수행할 수 있어서 범용적인 표준 최적화 툴로 자리매김 되고 있다. ADMM은 원래의 문제보다 최적화가 쉬운 부분문제로 분할하고 이를 취합함으로써 복잡한 원 문제를 해결하는 방식의 근사알고리즘이다. 부드럽지 않거나 복합적인 (composite) 목적 함수를 최적화할 때 유용하며, 쌍대이론과 proximal 작용소 이론을 토대로 체계적으로 알고리즘을 구성할 수 있기 때문에 통계 및 기계학습 분야에서 폭 넓게 활용되고 있다. 본 논문에서는 최근 통계와 관련된 여러 분야에서 ADMM알고리즘의 활용도를 살펴보고자 하며 주요한 두 가지 주제에 중점을 두고자 한다. (1) 목적식의 분할 전략과 증강 라그랑지안 방법 및 쌍대문제의 설명과 (2) proximal 작용소의 역할이다. 알고리즘이 적용된 사례로, 별점화 함수 추정 등의 조정화 (regularization)를 활용한 방법론들을 소개한다. 모의 자료를 활용하여 lasso 문제의 최적화에 대한 실증결과를 제시한다.

• 응용통계연구
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• 제35권2호
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• pp.265-283
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• 2022

사용자들의 영화정보를 기록한 MovieLens 데이터는 추천 시스템 연구에서 아이디어를 탐색하고 검증하는데 상당한 가치가 있는 데이터로, 기존 데이터 분할 및 군집화 알고리즘을 사용하여 사용자 평점 데이터를 기반으로 항목 집합을 분할하는 연구 등에 사용되는 데이터이다. 본 논문에서는 기존 연구에서 대표적으로 사용되었던 영화 평점 데이터와 영화 장르 데이터를 통해 사용자의 장르 선호도를 예측하여 선호도 패턴을 기반으로 사용자를 군집화(clustering)하고, 유의미한 정보를 얻는 연구를 진행하였다. MovieLens 데이터는 영화의 전체 개수에 비해 사용자별 평균 영화 평점 수가 낮아 결측 비율이 높다. 이러한 이유로 기존의 군집화 방법을 적용하는 데 한계가 존재한다. 본 논문에서는 MovieLens 데이터 특성에 모티브를 얻어 쌍별 규합 벌점함수(pairwise fused penalty)를 활용한 볼록 군집화(convex clustering) 기반의 방법을 제안한다. 특히 결측치 대체(missing imputation)도 동시에 해결하는 최적화 문제를 통해 기존의 군집화 분석과 차별화하였다. 군집화는 반복 알고리즘인 ADMM을 통해 제안하는 최적화 문제를 풀어 진행한다. 또한 시뮬레이션과 MovieLens 데이터 적용을 통해 제안하는 군집화 방법이 기존의 방법보다 노이즈 및 이상치에 상대적으로 민감하지 않은 것으로 보인다.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제15권8호
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• pp.3086-3101
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• 2021

To supply precise marketing and differentiated service for the electric power service department, it is very important to predict the customers with high sensitivity of electric power failure. To solve this problem, we propose a novel grouped 𝑙_1/2 sparsity constrained logistic regression method for sensitivity assessment of electric power failure. Different from the 𝑙₁ norm and k-support norm, the proposed grouped 𝑙_1/2 sparsity constrained logistic regression method simultaneously imposes the inter-class information and tighter approximation to the nonconvex 𝑙₀ sparsity to exploit multiple correlated attributions for prediction. Firstly, the attributes or factors for predicting the customer sensitivity of power failure are selected from customer sheets, such as customer information, electric consuming information, electrical bill, 95598 work sheet, power failure events, etc. Secondly, all these samples with attributes are clustered into several categories, and samples in the same category are assumed to be sharing similar properties. Then, 𝑙_1/2 norm constrained logistic regression model is built to predict the customer's sensitivity of power failure. Alternating direction of multipliers (ADMM) algorithm is finally employed to solve the problem by splitting it into several sub-problems effectively. Experimental results on power electrical dataset with about one million customer data from a province validate that the proposed method has a good prediction accuracy.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제12권5호
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• pp.2366-2395
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• 2018

Multi-view super-resolution (MVSR) refers to the process of reconstructing a high-resolution (HR) image from a set of low-resolution (LR) images captured from different viewpoints typically by different cameras. These multi-view images are usually obtained by a camera array. In our previous work [1], we super-resolved multi-view LR images via image fusion (IF) and blind deblurring (BD). In this paper, we present a new MVSR method that jointly realizes IF and BD based on an integrated energy function optimization. First, we reformulate the MVSR problem into a multi-channel blind deblurring (MCBD) problem which is easier to be solved than the former. Then the depth map of the desired HR image is calculated. Finally, we solve the MCBD problem, in which the optimization problems with respect to the desired HR image and with respect to the unknown blur are efficiently addressed by the alternating direction method of multipliers (ADMM). Experiments on the Multi-view Image Database of the University of Tsukuba and images captured by our own camera array system demonstrate the effectiveness of the proposed method.

• Journal of Communications and Networks
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• 제11권4호
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• pp.350-358
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• 2009

In a wireless sensor network (WSN) setting, this paper presents a distributed decision-making framework and illustrates its application in an online structural health monitoring (SHM) system. The objective is to recover a damage severity vector, which identifies, localizes, and quantifies damages in a structure, via distributive and collaborative decision-making among wireless sensors. Observing the fact that damages are generally scarce in a structure, this paper develops a nonlinear 0-norm minimization formulation to recover the sparse damage severity vector, then relaxes it to a linear and distributively tractable one. An optimal algorithm based on the alternating direction method of multipliers (ADMM) and a heuristic distributed linear programming (DLP) algorithm are proposed to estimate the damage severity vector distributively. By limiting sensors to exchange information among neighboring sensors, the distributed decision-making algorithms reduce communication costs, thus alleviate the channel interference and prolong the network lifetime. Simulation results in monitoring a steel frame structure prove the effectiveness of the proposed algorithms.

• 응용통계연구
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• 제37권3호
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• pp.265-282
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• 2024

기대 수익률은 높이고, 재무적 위험은 낮추는 것을 목표로 하는 금융 포트폴리오 최적화 분야에서는 위험 측정 지표에 관한 연구가 활발히 진행되어 왔다. 적은 자산으로 효율적인 포트폴리오를 구성하기 위해 다양한 페널티 항을 활용한 연구 또한 지속해서 진행되어 왔다. 본 논문에서는 평균-숏폴 포트폴리오와 SLOPE 페널티 항을 결합한 새로운 포트폴리오 최적화 식을 제안하였다. 이 과정에서 선형계획법으로 표현되지 않는 최적화식을 새로운 변수를 도입해 표현하고, 이를 ADMM 알고리즘을 사용해 해결하는 방식을 제안하였다. SLOPE 페널티 항이 갖는 그룹화 특징이 본 논문에서 제안하는 평균-숏폴 포트폴리오에서도 해당 특징이 유효함을 시뮬레이션 데이터를 바탕으로 확인하였다. 실증 데이터 분석을 통해서는 본 논문에서 제안한 모형을 기반으로 실제 투자 환경에서 고려할 수 있는 4가지 종류의 포트폴리오 구성 방식을 제안하고, 평가하였다.

• Structural Engineering and Mechanics
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• 제91권2호
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• pp.227-238
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• 2024

Sparse regularization methods have proven effective in addressing the ill-posed equations encountered in moving force identification (MFI). However, the complexity of vehicle loads is often ignored in existing studies aiming at enhancing MFI accuracy. To tackle this issue, a double 𝑙₁ regularization method is proposed for MFI based on a response spectrum-based weighted dictionary in this study. Firstly, the relationship between vehicle-induced responses and moving vehicle loads (MVL) is established. The structural responses are then expanded in the frequency domain to obtain the prior knowledge related to MVL and to further construct a response spectrum-based weighted dictionary for MFI with a higher accuracy. Secondly, with the utilization of this weighted dictionary, a double 𝑙₁ regularization framework is presented for identifying the static and dynamic components of MVL by the alternating direction method of multipliers (ADMM) method successively. To assess the performance of the proposed method, two different types of MVL, such as composed of trigonometric functions and driven from a 1/4 bridge-vehicle model, are adopted to conduct numerical simulations. Furthermore, a series of MFI experimental verifications are carried out in laboratory. The results shows that the proposed method's higher accuracy and strong robustness to noises compared with other traditional regularization methods.