Arieh Iserles is Professor of Numerical Analysis of Differential Equations at the University of Cambridge.

• 1. Mixed-integer nonlinear optimization Pietro Belotti, Christian Kirches, Sven Leyffer, Jeff Linderoth, James Luedtke and Ashutosh Mahajan; 2. High-dimensional integration: the quasi-Monte Carlo way Josef Dick, Frances Y. Kuo and Ian H. Sloan; 3. Finite element methods for surface PDEs Gerhard Dziuk and Charles M. Elliott; 4. Atomistic-to-continuum coupling Mitchell Luskin and Christoph Ortner; 5. On first-order algorithms for l1/nuclear norm minimization Yurii Nesterov and Arkadi Nemirovski.