Name
Abstract | ||
|---|---|---|
This note considers the inexact cubic-regularized Newtonu0027s method (CR), which has been shown in cite{Cartis2011a} to achieve the same order-level convergence rate to a secondary stationary point as the exact CR citep{Nesterov2006}. However, the inexactness condition in cite{Cartis2011a} is not implementable due to its dependence on future iterates variable. This note fixes such an issue by proving the same convergence rate for nonconvex optimization under an inexact adaptive condition that depends on only the current iterate. Our proof controls the sufficient decrease of the function value over the total iterations rather than each iteration as used in the previous studies, which can be of independent interest in other contexts. |
Year | Venue | Field |
|---|---|---|
2018 | arXiv: Optimization and Control | Applied mathematics,Discrete mathematics,Stationary point,Rate of convergence,Iterated function,Mathematics,Newton's method |
DocType | Volume | Citations |
Journal | abs/1808.07384 | 0 |
PageRank | References | Authors |
0.34 | 0 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Zhe Wang | 1 | 198 | 24.41 |
| Yi Zhou | 2 | 65 | 17.55 |
| Yingbin Liang | 3 | 1646 | 147.64 |
| Guanghui Lan | 4 | 1212 | 66.26 |