CMSA Q&A Seminar: What is a self-concordant barrier function?, and what is an accelerated first-order algorithm? (ICM Series: On the work of Yurii Nesterov)

The two most impactful contributions of Nesterov on both theory and computation in optimization are (i) self-concordant barriers for interior-point methods in convex optimization, and (ii) accelerated first-order methods for convex optimization. My own research in continuous optimization – and indeed my perspective on the field of mathematical optimization — has been profoundly impacted by Nesterov. In this talk I aim to explain these two contributions – self-concordant barriers and accelerated first-order methods – and how they have fundamentally improved optimization both computationally and theoretically.