Memory-Efficient Structured Convex Optimization via Extreme Point Sampling

Memory is a key computational bottleneck when solving large-scale convex optimization problems, such as semidefinite programs (SDPs). In this paper, we focus on the regime in which storing an $n\times n$ matrix decision variable prohibitive. To solve SDPs regime, develop randomized algorithm that returns random vector whose covariance near-feasible and near-optimal for SDP. We show how to by modifying Frank--Wolfe systematically replace iterates with vectors. As application of approach, implement Goemans--Williamson approximation MaxCut using $\mathcal{O}(n)$ memory addition required store problem instance. then extend our approach deal broader range structured replacing variables extreme points feasible region.