View abstract

Session II.2 - Continuous Optimization

Thursday, June 15, 15:30 ~ 16:00

A Newton-MR Algorithm With Complexity Guarantees for Nonconvex Optimization

Fred Roosta

University of Queensland, Australia   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

We consider variants of Newton-MR algorithm for solving unconstrained, smooth, but non-convex optimization problems. Unlike the overwhelming majority of Newton-type methods, which rely on conjugate gradient algorithm as the primary workhorse for their respective sub-problems, Newton-MR employs minimum residual (MINRES) method. Recently, it has been established that MINRES has inherent ability to detect non-positive curvature directions as soon as they arise and certain useful monotonicity properties will be satisfied before such detection. We leverage these recent results and show that our algorithms come with desirable properties including competitive first and second-order worst-case complexities. Numerical examples demonstrate the performance of our proposed algorithms.

Joint work with Yang Liu (Oxford University).

View abstract PDF