We introduce a Swarm-Based Random Descent (SBRD) method for non-convex optimization. The swarm consists of agents, identified with positions, x, and masses, m.  There are three key aspects to the SBRD dynamics: (i) persistent transition of mass from high to lower ground; (ii) marching along the gradient descent: an m-dependent random choice of marching direction aligned with the orientation of gradient descent; and (iii) a time stepping protocol, h(x, m), which decreases with m.

The interplay between positions and masses leads to dynamic distinction between ‘leaders’ and ‘explorers’: heavier agents lead the swarm near local minima with small time steps; lighter agents explore the landscape in random directions with large(r) time steps, and lead to improved position, i.e., reduce the ‘loss’ for the swarm. Convergence analysis and numerical simulations demonstrate the effectiveness of SBRD method as a global optimizer.

Eitan Tadmor is a Distinguished University Professor at the University of Maryland, College Park, where he served as the Director of the Center for Scientific Computation and Mathematical Modeling (CSCAMM), 2002–2016. He held professorship positions at Tel-Aviv University, 1983–1995, and at UCLA, 1995–2002, where he was the founding co-director of the NSF Institute for Pure and Applied Mathematics (IPAM), 1999–2001. In 2016–2017 he was a Senior Fellow at the Institute for Theoretical Studies at ETH-Zurich (ETH-ITS).

Tadmor was the PI for NSF Focus Research Group on “Kinetic Description of Multiscale Phenomena”, 2008–2012, and NSF Research network “Kinetic Description of Emerging Challenges in Natural Sciences” (Ki-Net), 2012–2020.

Tadmor gave a 2002 invited ICM address in Beijing, a SIAM invited JMM address in 2014, a 2019 plenary ICIAM lecture in Valencia, and the 2022 AMS Josiah Willard Gibbs Lecture. He was awarded the SIAM–ETH Peter Henrici Prize in 2015 and the AMS–SIAM Norbert Wiener Prize in Applied Mathematics in 2022. Tadmor is an AMS and SIAM Fellow and a member of the European Academy of Science.