Numerical Optimization

With Eitan Tadmor and Jingcheng Lu, I study swarm-based methods for non-convex optimization. The methods use communicating agents whose positions and masses evolve together: mass transfer favors agents with lower objective values, while the agents’ masses control their step sizes.

Publications

Swarm-Based Gradient Descent Method for Non-Convex Optimization (Communications of the American Mathematical Society, 2024) introduces the method, combining convergence analysis with numerical benchmarks.

With Eitan Tadmor, I extend the approach to randomized descent directions in Swarm-Based Optimization with Random Descent (Acta Applicandae Mathematicae, 2024), allowing agents to explore directions around the gradient while preserving descent.

Software

The SwarmPy documentation introduces the algorithms and provides code and examples.