서브메뉴
검색
Stability of First-Order Methods in Tame Optimization
Stability of First-Order Methods in Tame Optimization
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20250211151331
- ISBN
- 9798382791906
- DDC
- 519
- 저자명
- Lai, Lexiao.
- 서명/저자
- Stability of First-Order Methods in Tame Optimization
- 발행사항
- [Sl] : Columbia University, 2024
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2024
- 형태사항
- 83 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 85-12, Section: B.
- 주기사항
- Advisor: Josz, Cedric.
- 학위논문주기
- Thesis (Ph.D.)--Columbia University, 2024.
- 초록/해제
- 요약Modern data science applications demand solving large-scale optimization problems. The prevalent approaches are first-order methods, valued for their scalability. These methods are implemented to tackle highly irregular problems where assumptions of convexity and smoothness are untenable.Seeking to deepen the understanding of these methods, we study first-order methods with constant step size for minimizing locally Lipschitz tame functions. To do so, we propose notions of discrete Lyapunov stability for optimization methods. Concerning common first-order methods, we provide necessary and sufficient conditions for stability. We also show that certain local minima can be unstable, without additional noise in the method. Our analysis relies on the connection between the iterates of the first-order methods and continuous-time dynamics.
- 일반주제명
- Applied mathematics
- 일반주제명
- Computer science
- 키워드
- Lipschitz tame
- 기타저자
- Columbia University Operations Research
- 기본자료저록
- Dissertations Abstracts International. 85-12B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
008250123s2024 us c eng d■001000017161259
■00520250211151331
■006m o d
■007cr#unu||||||||
■020 ▼a9798382791906
■035 ▼a(MiAaPQ)AAI31241102
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a519
■1001 ▼aLai, Lexiao.
■24510▼aStability of First-Order Methods in Tame Optimization
■260 ▼a[Sl]▼bColumbia University▼c2024
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2024
■300 ▼a83 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 85-12, Section: B.
■500 ▼aAdvisor: Josz, Cedric.
■5021 ▼aThesis (Ph.D.)--Columbia University, 2024.
■520 ▼aModern data science applications demand solving large-scale optimization problems. The prevalent approaches are first-order methods, valued for their scalability. These methods are implemented to tackle highly irregular problems where assumptions of convexity and smoothness are untenable.Seeking to deepen the understanding of these methods, we study first-order methods with constant step size for minimizing locally Lipschitz tame functions. To do so, we propose notions of discrete Lyapunov stability for optimization methods. Concerning common first-order methods, we provide necessary and sufficient conditions for stability. We also show that certain local minima can be unstable, without additional noise in the method. Our analysis relies on the connection between the iterates of the first-order methods and continuous-time dynamics.
■590 ▼aSchool code: 0054.
■650 4▼aApplied mathematics
■650 4▼aComputer science
■653 ▼aData science applications
■653 ▼aOptimization methods
■653 ▼aFirst-order methods
■653 ▼aLipschitz tame
■690 ▼a0796
■690 ▼a0984
■690 ▼a0364
■71020▼aColumbia University▼bOperations Research.
■7730 ▼tDissertations Abstracts International▼g85-12B.
■790 ▼a0054
■791 ▼aPh.D.
■792 ▼a2024
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17161259▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
