In this paper we propose two modifications to Nesterov's algorithms for minimizing convex functions in relative scale. The first is based on a bisection technique and leads to improved theoretical iteration complexity, and the second is a heuristic for avoiding restarting behavior. The fastest of our algorithms produces a solution within relative error O(1/k) of the optimum, with k being the iteration counter.
- convex optimization
- relative scale
- Nesterov's smoothing technique
- Lowner-John ellipsoids
- minimum volume enclosing ellipsoids