Recent Advances in Convex Optimization

Опубликовано 6 сентября 2016, 17:59

Convex optimization is now widely used in control, signal processing, networking, communications, machine learning, finance, combinatorial optimization, and other fields. For many problem classes reliable general purpose solvers are now available, with development of new algorithms and implementations continuing at a rapid pace. In this talk I will give an overview of some recent advances. The first is the development of specification and modeling languages specifically for convex optimization. These languages allow very rapid development of applications based on convex optimization, and enhance learning and teaching of the methods. The second is the development of methods for extremely large convex problems, with millions (or more) of variables and constraints, for specific families of problems arising in applications. Truncated Newton interior-point methods, with well-chosen pre-conditioner, can solve far larger problems than generic methods. The third advance is in the area of algorithms for fast solution of convex optimization problems, for use in real-time and embedded applications. (Joint work with Michael Grant, Kwangmoo Koh, Seung-Jean Kim, Yang Wang)