Mathematics Colloquia and Seminars

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In this talk, we will present Fenchel duality, the convex conjugate, and how these concepts are used in the context of first-order smooth convex interpolation (based on the paper "Smooth strongly convex interpolation and exact worst-case performance of first-order methods"). We will then discuss an alternative construction for the same result (based on results from "The exact information-based complexity of smooth convex minimization") and show how it resolves to the question of non-negative smooth interpolation in the convex and non-convex setting. Time permitting, we will discuss the connection between these results and the performance of first-order optimization methods.