I am currenty a professor in computer science at the University of British Columbia (Okanagan campus).
My research is at the boundary between Mathematics and Computer Science and is roughly split into 2 directions:
- designing new algorithms in Computer-Aided Convex Analysis to compute operators arising in convex analysis. The focus is on building tools to manipulate fundamental convex analysis objects thereby giving more insight into the structure of optimization problems. The field is conveniently summarized as Computational Convex Analysis and involves investigating hybrid symbolic-numerical algorithms.
I have been developing the CCA toolbox to compute fundamental transforms of convex analysis under Scilab. Computational geometry algorithms form the core of the techniques. The scope of the library has been slowy expanded beyong convex analysis to cover monotone operators, and nonsmooth (nonconvex) analysis. Only basic programming skills are needed to contribute to that area with a very wide field of applications (image processing, network communication, PDE, etc.).
Visualizing operators is an ongoing challenge considering the interesting operators are set-valued and require 4 dimensions to visualize. Virtual Reality is a technology I am exploring to provide intuitive interactive visualization.
- modeling and applications of optimization. My main project focuses on designing a road at minimal cost while still satisfying regulatory and safety constraints. It is a collaboration with colleagues in mathematics, statistics, and engineering; and in partnership with a private company.
The road design problem usually split into the horizontal, vertical, and earth-moving subproblems. It is a large-scale global optimization problem. Some programming experience is really helpful to contribute to that project (and producing good well documented code). Numerical experiments will be performed on multi-core workstations or clusters using state of the art optimization software.
Keywords: Computational Science and Engineering, computational mathematics, convex analysis, numerical optimization, modelling, and applications.
I am looking for graduate students who are interested in these topics. If you are interested, please contact me and consider applying to our graduate programs: MSc in Computer Science and MSc/PhD in Interdisciplinary Graduate Studies, especially the Optimization theme. (There are ongoing graduate funding opportunities; apply here.)
Join the Centre for Optimization Convex Analysis and Nonsmooth Analysis, an active, fun, small, but dedicated group of researchers and students with interest in Optimization and Analysis. Enjoy campus life in the beautiful city of Kelowna, at the shores of Lake Okanagan, and nestled right between the Rocky Mountains and Vancouver.