• 융합신호처리학회논문지
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• 제6권2호
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• pp.82-88
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• 2005

본 논문은 선형적으로 파라미터화된 시스템에 대한 보상방식을 제안한다. 이 보상기는 전형적인 선형 제어기와 적분형의 적응법칙을 갖는 적응 관측기로 구성되며 이 때 적응법칙은 SG 알고리즘에 근거하여 설계된다. 제안된 보상전략에서는 다른 여러 연구에서 제안된 중간함수 대신에 growth조건, convex조건, attainability조건, 그리고 pseudo gradient 조건을 만족하는 함수들로 적응법칙이 설계된다. 제안된 방식은 추적오차에 대한 점근적 안정도 및 파라미터에 대한 추정오차의 bounded stability를 만족한다. 예제를 통하여 제안된 보상방식의 타당성을 보인다. 그리고 기존의 방식인 Huang의 방법과의 비교를 통해 제안된 방식이 정상상태에서의 파라미터 오차가 더 작아짐을 보인다.

• 대한수학회보
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• 제45권3호
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• pp.523-561
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• 2008

The purpose of this paper is to survey the use of the important method of scaling in analysis, and particularly in complex analysis. Applications are given to the study of automorophism groups, to canonical kernels, to holomorphic invariants, and to analysis in infinite dimensions. Current research directions are described and future paths indicated.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제8권2호
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• pp.153-162
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• 2001

In this Paper, the notion of $\varepsilon$-Birkhoff orthogonality introduced by Dragomir [An. Univ. Timisoara Ser. Stiint. Mat. 29(1991), no. 1, 51-58] in normed linear spaces has been extended to metric linear spaces and a decomposition theorem has been proved. Some results of Kainen, Kurkova and Vogt [J. Approx. Theory 105 (2000), no. 2, 252-262] proved on e-near best approximation in normed linear spaces have also been extended to metric linear spaces. It is shown that if (X, d) is a convex metric linear space which is pseudo strictly convex and M a boundedly compact closed subset of X such that for each $\varepsilon$>0 there exists a continuous $\varepsilon$-near best approximation $\phi$ : X → M of X by M then M is a chebyshev set .

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1996년도 한국자동제어학술회의논문집(국내학술편); 포항공과대학교, 포항; 24-26 Oct. 1996
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• pp.466-469
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• 1996

In this paper, we present the global minimization condition by an informal analysis of the Langevine competitive learning neural network. From the viewpoint of the stochastic process, it is important that competitive learning guarantees an optimal solution for pattern recognition. By analysis of the Fokker-Plank equation for the proposed neural network, we show that if an energy function has a special pseudo-convexity, Langevine competitive learning can find the global minima. Experimental results for pattern recognition of handwritten numeral data indicate the superiority of the proposed algorithm.

• 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.