Papers:

• Using orthogonally structured positive bases for constructing positive k-spanning sets with cosine measure guarantees (Link!)
Joint work with Clément Royer, Gabriel Jarry-Bolduc and Warren Hare. Published in Linear Algebra and its applications.

Positive spanning sets (PSSs) can be defined as sets properly approximating any given direction in the space. Optimization methods based on PSSs typically favor those with the best cosine measure. However, there is no easy way to compute this measure for an arbitrary set.
This paper shows how the cosine measure of some specific positive spanning sets (called OSPB) can be computed in polynomial time. Using OSPBs, it also shows how to create resilient PSSs whose cosine measure remains large enough after removing some elements.

Conferences:

• Derivative Free Optimization Symposium (Kelowna, 2022).
• Siam Conference on Optimization (Seattle, 2023).
• Optimization (Aveiro, 2023).