Consensus-Based optimization

Nonconvex and nonsmooth optimization problems are ubiquitous across science and technology, appearing whenever models must capture complex real-world phenomena involving nonlinear interactions and structural constraints, from the extremely hard problem of protein folding to the computation of optimal operations of (humanoid) robots. Heuristics and local optimization methods are heavily used in practice, with limited success and often no theoretical guarantees. Establishing methods that can provably solve nonconvex optimization would open the door to approaching problems that currently remain inaccessible to rigorous mathematical analysis.