Nonconvex optimization and jamming

Recent work on the jamming transition of particles with short-range interactions has drawn connections with models based on minimization problems with linear inequality constraints and a concave objective. These properties reduce the continuous optimization problem to a discrete search among the corners of the feasible polytope. I will discuss results from simulations of models with and without quenched disorder, exhibiting critical power laws, scaling collapse, and protocol dependence. These models are also well-suited for study using tools of algebraic topology, which I will discuss briefly.