In this talk, we describe a transformation, which was recently proposed by Jim Renegar, that can convert wildly non-Lipchitz convex functions into Lipschitz ones. Based on this, we present a first-order algorithm for solving non-smooth, non-Lipschitz convex optimization problems. At each iteration, our algorithm takes a subgradient step and then does a radial projection to ensure feasibility. This procedure completely avoids computing costly orthogonal projections, typical of subgradient methods. In the case of semidefinite optimization, this replaces solving a hard feasibility problem at each iteration with eigenvector computations.