Prof. Nicolas Boumal Receives 2026 SIAM Optimization Best Paper Prize

Every three years, the Society for Industrial and Applied Mathematics (SIAM) presents its Activity Group on Optimization Best Paper Prize to the author or authors of an outstanding paper in optimization published within the preceding four calendar years. This year, the prize recognizes work that Boumal and McRae carried out together during McRae's postdoc at EPFL.

Their paper, "Benign Landscapes of Low-Dimensional Relaxations for Orthogonal Synchronization on General Graphs," addresses orthogonal synchronization: the problem of estimating a set of orthogonal matrices — such as rotations — from pairwise measurements. This class of problems arises in robotics, computer vision, and network analysis. A standard formulation leads to a nonconvex optimization problem, which is computationally challenging. Convex relaxations can overcome this difficulty, but they significantly increase the number of variables, which limits their practicality for large-scale problems.

Boumal and McRae show that a more compact nonconvex relaxation is sufficient. Despite its nonconvexity, this relaxation has a benign landscape: all second-order critical points are global optima.

The result connects two areas of applied mathematics. In optimization, it builds on earlier work and helps explain empirical observations reported in robotics applications. In dynamical systems and control theory, it is related to the Kuramoto oscillator and resolves an open question posed in that context. "This work belongs to two distinct areas of applied mathematics and resolves an open question that was separately posed in quite different language in both areas," the authors said. "We are happy and honored that the SIAM Activity Group on Optimization has found it worthy of the Best Paper Prize."

Andrew McRae will present the paper at the 2026 SIAM Conference on Optimization on June 4. Nicolas Boumal is an associate professor at EPFL, where his research focuses on continuous optimization and includes contributions to the Manopt toolbox for optimization on manifolds. Andrew McRae is now a researcher at the École nationale des ponts et chaussées (ENPC) in France.