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Linear Constraints in Optimal Transport
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| 자료유형 | 학위논문 |
|---|---|
| 서명/저자사항 | Linear Constraints in Optimal Transport. |
| 개인저자 | Stebegg, Florian. |
| 단체저자명 | Columbia University. Statistics. |
| 발행사항 | [S.l.]: Columbia University., 2019. |
| 발행사항 | Ann Arbor: ProQuest Dissertations & Theses, 2019. |
| 형태사항 | 284 p. |
| 기본자료 저록 | Dissertations Abstracts International 81-02B. Dissertation Abstract International |
| ISBN | 9781085688277 |
| 학위논문주기 | Thesis (Ph.D.)--Columbia University, 2019. |
| 일반주기 |
Source: Dissertations Abstracts International, Volume: 81-02, Section: B.
Advisor: Nutz, Marcel F. |
| 이용제한사항 | This item must not be sold to any third party vendors.This item must not be added to any third party search indexes. |
| 요약 | This thesis studies the problem of optimal mass transportation with linear constraints -- supermartingale and martingale transport in discrete and continuous time. Appropriate versions of corresponding dual problems are introduced and shown to satisfy fundamental properties: weak duality, absence of a duality gap, and the existence of a dual optimal element. We show how the existence of a dual optimizer implies that primal optimizers can be characterized geometrically through their support -- an infinite dimensional analogue of complementary slackness. In discrete time martingale and supermartingale transport problems, we utilize this result to establish the existence of canonical transport plans, that is joint optimizers for large families of reward functions. To this end, we show that the optimal support coincides for these families. We additionally characterize these transport plans through order-theoretic minimality properties, with respect to second stochastic order and convex order, respectively, in the supermartingale and the martingale case. This characterization further shows that the canonical transport plan is unique. |
| 일반주제명 | Statistics. |
| 언어 | 영어 |
| 바로가기 | 
: 이 자료의 원문은 한국교육학술정보원에서 제공합니다. |
