Name
Abstract | ||
|---|---|---|
Second-order methods, which utilize gradients as well as Hessians to optimize a given function, are of major importance in mathematical optimization. In this work, we prove tight bounds on the oracle complexity of such methods for smooth convex functions, or equivalently, the worst-case number of iterations required to optimize such functions to a given accuracy. In particular, these bounds indicate when such methods can or cannot improve on gradient-based methods, whose oracle complexity is much better understood. We also provide generalizations of our results to higher-order methods. |
Year | DOI | Venue |
|---|---|---|
2019 | 10.1007/s10107-018-1293-1 | Mathematical Programming |
Keywords | Field | DocType |
Smooth convex optimization,Oracle complexity,90C25,65K05,49M37 | Applied mathematics,Mathematical optimization,Oracle,Proximal Gradient Methods,Subderivative,Conic optimization,Proper convex function,Convex optimization,Ellipsoid method,Linear matrix inequality,Mathematics | Journal |
Volume | Issue | ISSN |
178.0 | 1-2 | 1436-4646 |
Citations | PageRank | References |
4 | 0.42 | 8 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Yossi Arjevani | 1 | 34 | 5.55 |
| Ohad Shamir | 2 | 1627 | 119.03 |
| Ron Shiff | 3 | 4 | 0.42 |