Room 505, Cosmology Building, NTU
Gateway to the World-Student Presentation after Academic Visits Abroad (學術報告)
時間: 2025年11月12日(三) 10:00 ~ 11:00
地點: 台灣大學次震宇宙館 505 教室
報告人: 徐睿安 (NTU)
線上參與: https://nationaltaiwanuniversity-ksz.my.webex.com/nationaltaiwanuniversity-ksz.my/j.php?MTID=m2a0de3d074506831b2f8f96daca3dbd0
【Title】A Primer on Optimal Transport
【Abstract】Optimal Transport (OT) provides a unifying mathematical framework for comparing and transforming probability distributions, bridging geometry, analysis, and applications in data science. This talk introduces the foundational ideas of OT, starting from Monge’s classical formulation of minimizing the total cost of moving mass from one distribution to another, and proceeds to Kantorovich’s relaxation, which turns the problem into a convex optimization over couplings.
We then discuss the geometric characterization of optimality via c-cyclical monotonicity, the dual formulation involving potential functions (Kantorovich potentials), and the emergence of c-concave structures that parallel convex analysis. Special attention is given to the quadratic cost case, leading to Brenier’s theorem and the Monge–Ampère equation, which link OT to partial differential equations and convex geometry.
【註】徐睿安於2025年6月9日至20日參加在SLMath 舉辦的 "Statistical Optimal Transport (SLMath)" 課程
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