Academic advisor: Anders Forsgren
Sponsor: Swedish Research Council (VR)
The proposed project concerns further development of methods for solving large-scale nonlinear optimization problems. The methods considered are based on Newton's method. They may be full Newton methods, that make use of second-derivative information, or quasi-Newton methods, that approximate the second-derivative information. Our interest in quasi-Newton method is motivated by a ``traditional'' reason, as a method that does not require second-derivative information, but also by its regularizing behavior on certain ill-conditioned problems. We believe that this insight into the behavior of quasi-Newton methods can lead to significant improvement in terms of limited-memory quasi-Newton methods.
We also have more applied projects towards optimization of radiation therapy (with RaySearch Laboratories) and optimization of telecommunications networks (with Ericsson). There is a strong interplay between the applications and the fundamental research. The abovementioned regularizing behavior was an outcome of the research on radiation therapy. The research direction of the graduate student position in question here is towards fundamental method research, but there will be close connections to more applied areas. Numerical linear algebra will be a major component in the research, as efficient solution of particular systems of linear equations are of utmost importance in this research.
This project is suitable for candidates with an interest for numerical optimization and numerical linear algebra.