日時：12/12(金) 14:00-
場所：8号館 213号室（数理会議室）
講演者：Andrew Calcan
タイトル：（下記英文タイトル参照）
アブストラクト：（下記英文アブストラクト参照）
講演者：Jordan Collard
タイトル：（下記英文タイトル参照）
アブストラクト：（下記英文アブストラクト参照）
Date: 12/12(Friday) 1400-
Location: Room 213, Research Bldg. No. 8
Speaker: Andrew Calcan
Title: the alternating direction method of multipliers for manifold and nonconvex optimisation
Abstract: The alternating direction method of multipliers (ADMM) is one of the most popular algorithms in modern optimisation. In this talk, I aim to give accessible introductions to ADMM and its relationship with Douglas–Rachford splitting. We will use this relationship to provide insight into ADMM’s convergence, including its behaviour in the nonconvex setting. We will also discuss two recent directions that push ADMM beyond its classical convex origin: an extension to manifold optimisation, and a homotopy-based variant for challenging nonconvex problems.
Speaker: Jordan Collard
Title: Projection methods and their applications to nonconvex feasibility problems
Abstract: This talk explores projection algorithms for feasibility problems, with an emphasis on settings that go beyond classical convex theory. We discuss the Douglas–Rachford method, the circumcentered-reflection method, and the Lyapunov surrogate method, and illustrate their behaviour on a range of continuous and discrete models. Particular attention is given to problems arising in graph colouring and related combinatorial formulations. Throughout, we highlight structural features that help explain the surprising effectiveness of these algorithms.