A Low-Rank ​Augmented Lagrangian Frank-Wolfe-Based ​Method for SDPs with Unbounded Feasible Regions​

Abstract: We present HALLaR+, a first-order method for large-scale semidefinite programs with equality and inequality constraints. Unlike existing low-rank methods, HALLaR+ does not require compact feasible regions or trace constraints. The method combines augmented Lagrangian optimization with hybrid Frank-Wolfe steps and achieves strong theoretical guarantees and competitive performance across diverse SDP benchmarks.​