- Series
- School of Mathematics Colloquium
- Time
- Friday, October 2, 2026 - 11:00am for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Eitan Tadmor – University of Maryland – https://www.math.umd.edu/~tadmor/
- Organizer
- Harold Blum
We discuss a novel class of swarm-based gradient descent (SBGD) methods for nonconvex optimization. Each agent in the swarm is characterized by its position and mass. The dynamics combines two mechanisms: persistent transfer of mass from agents positioned on “higher ground” to those with lower objective values, and a mass-dependent time-stepping protocol. This coupling creates a dynamic distinction between “leaders” and “explorers.” Heavier agents act as leaders, use small time steps to refine promising regions near local minima, while light agents take larger steps, exploring the landscape for lower objective values. The swarm dynamics adaptively balances exploitation of local refinement with global exploration. We present convergence results and numerical experiments illustrating the effectiveness of SBGD for global optimization.