Streaming Solutions for Time-Varying Optimization Problems - Justin Romberg - FFT Apr 18th 2022
Abstract:
We will discuss streaming optimization problems where the goal is to minimize a sum of functions indexed by time. At each time step, a new function is introduced along with a new set of optimization variables; the function depends the optimization variables at the current time step and the previous one. Problems of this type arise in state estimation problems, including simultaneous localization and mapping (SLAM) in robotics, and in streaming reconstruction problems in signal processing.
We will give structural conditions under which solutions to these problems converge quickly in time. This leads directly to algorithms that have guaranteed performance while using limited memory. We will also show how our framework can be generalized to optimization programs organized on general graphs, where the vertices are associated with functions and the edges are associated with shared variables.
This is joint work with Tomer Hamam.