CDT in Data Science/School of Mathematics Seminar Talk

24 Jan 2017

All Hands Meetings on Big Data Optimization

Venue: School of Mathematics, James Clerk Maxwell Building, Kings Buildings, room 5323 (5th floor)

Date:  24th January 2017
Time: 12:15-13:30, as usual, lunch is provided
Speaker: Prof Ion Necoara (Bucharest)
Title: Linear convergence of first order methods for non-strongly convex optimization
Abstract: The standard assumption for proving linear convergence of first order methods for smooth convex optimization is the strong convexity of the objective function, an assumption which does not hold for many practical applications. In this paper, we derive linear convergence rates of several first order methods for solving smooth non-strongly convex constrained optimization problems, i.e. involving an objective function with a Lipschitz continuous gradient that satisfies some relaxed strong convexity condition. In particular, in the case of smooth constrained convex optimization, we provide several relaxations of the strong convexity conditions and prove that they are sufficient for getting linear convergence for several first order methods such as projected gradient, fast gradient and feasible descent methods. We also provide examples of functional classes that satisfy our proposed relaxations of strong convexity conditions. Finally, we show that the proposed relaxed strong convexity conditions cover important applications ranging from solving linear systems, Linear Programming, and dual formulations of linearly constrained convex problems.
This is joint work with Yurii Nesterov (Louvain) and Francois Glineur (Louvain)
Organizers: Nicolas Loizou and Peter Richtárik
Thanks to CDT in Data Science and School of Mathematics for support