Optimization in Theory and Practice

Speaker: Professor Steven Wright

Affiliation: University of Wisconsin-Madison

Abstract

Algorithms for continuous optimization problems have a rich history of design and innovation over the past several decades, in which mathematical analysis of their convergence and complexity properties plays a central role. Such algorithms are interesting not only for their theoretical properties but also for their practical usefulness as computational tools for solving real-world problems. There are often gaps between the practical performance of an algorithm and what can be proved about it. These two facets of the field - the theoretical and the practical - interact in fascinating ways, each driving innovation in the other. This talk surveys the development of algorithms in two areas — linear programming and unconstrained minimization of smooth functions — outlining major algorithm classes in each area along with their theoretical properties and practical performance, and highlighting how advances in theory and practice have influenced each other.

 A version of this talk will be given as an ICM plenary lecture in July, 2026.

Bio

Stephen J. Wright is the George B. Dantzig Professor of Computer Sciences at the University of Wisconsin-Madison, where his research focuses on computational optimisation and its applications in machine learning, data science, and other areas of science and engineering. He is the author or co-author of several widely used optimisation texts, including Primal-Dual Interior-Point Methods and, with Jorge Nocedal, Numerical Optimization. His contributions span optimisation theory, algorithms, software, and applications, and he has received major honours including the George B. Dantzig Prize, the INFORMS Khachiyan Prize, a NeurIPS Test of Time Award, and election to the National Academy of Engineering.