Structure Beyond Nonconvexity: Hidden Geometry in Optimization, Control, and Operations

Many foundational models in operations and control lead to optimization problems that are formally nonconvex, yet simple first-order methods often perform remarkably well in practice. This talk explains why by identifying structural features that make these problems effectively more tractable than their formulations suggest.

I will present two recent theoretical developments: (i) a characterization of the optimization landscape for policy-gradient methods in finite-horizon MDPs, and (ii) a hidden convexity phenomenon in queueing control. In both settings, I highlight verifiable conditions under which the objective satisfies a Polyak–Łojasiewicz–type condition, which in turn yields global convergence guarantees for gradient-based algorithms. I will show how these insights exploit structural features in classical operations models—such as base-stock inventory systems and cash-balance control—providing a unified explanation for why first-order methods can be reliable in complex stochastic systems.