Yves Lucet

Professor

Computer Science, Mathematics

Office: ASC 350
Phone: 250.807.9505
Email: yves.lucet@ubc.ca

Research Summary

Computational mathematics, optimization and convex analysis; modeling; model road design to minimize construction costs under safety and environmental constraints; creating algorithms for computer-aided convex analysis; visualizing operators in 2D, 3D, and 4D.

Courses & Teaching

Optimization; data structures.

Websites

https://people.ok.ubc.ca/ylucet

Degrees

PhD University of Toulouse

Research Interests & Projects

My research is at the boundary between Mathematics and Computer Science and is roughly split into two 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 slowly expanded beyond 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 is 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.

All the above projects are funded by NSERC.

Selected Publications & Presentations

Google Scholar

Professional Services/Affiliations/Committees

Director, Centre for Optimization, Convex Analysis and Nonsmooth Analysis