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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2024.3
- 수록면
- 395 - 408 (14page)
- DOI
- 10.4134/JKMS.j230284
이용수
초록· 키워드
오류제보하기
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 $C^2$ 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.
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