Convex Analysis at Infinity - An Introduction to Astral Space

Attend a distinguished seminar exploring the mathematical theory of convex functions that can only be minimized at infinity through the innovative concept of astral space. Learn about this compact extension of Euclidean space that incorporates points at infinity while maintaining the continuous extension of all linear functions. Discover how astral space, despite not being a vector space or metric space, possesses sufficient structure to meaningfully extend fundamental concepts including convexity, conjugacy, and subdifferentials. Examine the detailed structure of minimizers for convex functions on astral space, explore exact characterizations of continuity, and understand the convergence properties of descent algorithms in this extended mathematical framework. The presentation covers joint research with Miroslav Dudík and Matus Telgarsky, offering insights into advanced optimization theory and its applications. Gain exposure to cutting-edge mathematical research from a leading expert in theoretical and applied machine learning, including practical implications for understanding optimization problems where traditional Euclidean approaches fall short.