• 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.

• Journal of the Korean Data and Information Science Society
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• v.27 no.2
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• pp.381-394
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• 2016

Graphical model represents conditional dependencies between variables as a graph with nodes and edges. It is widely used in various fields including physics, economics, and biology to describe complex association. Conditional dependencies can be estimated from a inverse covariance matrix, where zero off-diagonal elements denote conditional independence of corresponding variables. This paper proposes a efficient BCDR (block coordinate descent with random permutation) algorithm using graphics processing units and random permutation for the CONCORD (convex correlation selection method) based on the BCD (block coordinate descent) algorithm, which estimates a inverse covariance matrix based on pseudo-likelihood. We conduct numerical studies for two network structures to demonstrate the efficiency of the proposed algorithm for the CONCORD in terms of computation times.

• Proceedings of the KIEE Conference
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• 2008.07a
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• pp.532-533
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• 2008

연계지역 전력시장 간의 에너지 거래는 전체 전력시장의 사회적 편익을 향상시키기 위해 이루어진다. 기존의 연계지역 전력시장 간시장 최적화 문제를 다루는 중앙처리 접근방식은 경쟁적 전력시장 환경하에서 적합한 모델이 아니다. 본 논문은 연계지역 전력시장 문제를 다루기 위해 보완 라그랑지안 승수 기법(Augmented Lagrangian Relaxation) 기반의 분산처리 최적화 방법을 제시한다. Block Coordinate Descent(BCD) 분산처리 기법이 보완 라그랑지안 승수의 최적화 문제를 분리하기 위해 적용된다. 연계시장 모델을 구현한 사례연구를 통해 제시된 알고리즘의 효용성을 입증한다.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.25 no.3
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• pp.107-116
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• 2021

We introduce optimization algorithms using Bregman Divergence for solving non-negative matrix factorization (NMF) problems. Bregman divergence is known a generalization of some divergences such as Frobenius norm and KL divergence and etc. Some algorithms can be applicable to not only NMF with Frobenius norm but also NMF with more general Bregman divergence. Matrix Factorization is a popular non-convex optimization problem, for which alternating minimization schemes are mostly used. We develop the Bregman proximal gradient method applicable for all NMF formulated in any Bregman divergences. In the derivation of NMF algorithm for Bregman divergence, we need to use majorization/minimization(MM) for a proper auxiliary function. We present algorithmic aspects of NMF for Bregman divergence by using MM of auxiliary function.