## Department Colloquium

### Friday, March 6th, 2020

**Time:** 2:30 p.m. **Place:** Jeffery Hall 234

**Speaker:** Tim Hoheisel (McGill University)

**Title:** Cone-Convexity and Composite Functions.

**Abstract: ** In this talk we provide a full conjugacy and subdifferential calculus for convex convex-composite functions in finite-dimensional space. Our approach, based on infimal convolution and cone-convexity, is straightforward. The results are established under a verifiable Slater-type condition, with relaxed monotonicity and without lower semicontinuity assumptions on the functions in play. The versatility of our findings is illustrated by a series of applications in optimization and matrix analysis, including conic programming, matrix-fractional, variational Gram, and spectral functions.

**Tim Hoheisel** is an Assistant Professor within the Department of Mathematics and Statistics at McGill University. He obtained his Ph.D. in Mathematics from the University of Wuerzburg in 2009. His research lies at the intersection of continuous optimization and nonsmooth analysis and therefore between applied and pure mathematics. The problems on which he works on can be motivated by concrete applications as well as purely conceptual interest.