A Subgradient Solution to Structured Robust Least Squares Problems

A standard and established method for solving a Least Squares problem in the presence of a structured uncertainty is to assemble and solve a semidefinite programming (SDP) equivalent problem. When the problem's dimensions are high, the solution of the structured robust least squares (RLS) problem via SDP becomes an expensive task in a computational complexity sense. We propose a subgradient based solution that utilizes the MinMax structure of the problem. This algorithm is justified by Danskin's MinMax Theorem and enjoys the well-known convergence properties of the subgradient method. The complexity of the new scheme is analyzed and its efficiency is verified by simulations of a robust equalization design.