- Convergence of first-order methods via the convex conjugate Javier Pena(jfpandrew.cmu.edu) Abstract: This paper gives a unified and succinct approach to the $O(1/\sqrt{k}), O(1/k),$ and $O(1/k^2)$ convergence rates of the subgradient, gradient, and accelerated gradient methods for unconstrained convex minimization. In the three cases the proof of convergence follows from a generic bound defined by the convex conjugate of the objective function. Keywords: First-order methods, convex conjugate Category 1: Convex and Nonsmooth Optimization (Convex Optimization ) Citation: Working Paper, Carnegie Mellon University Download: [PDF]Entry Submitted: 07/27/2017Entry Accepted: 07/27/2017Entry Last Modified: 07/27/2017Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.