Name
Abstract | ||
|---|---|---|
In this paper, a Riemannian BFGS method is defined for minimizing a smooth function on a Riemannian manifold endowed with a retraction and a vector transport. The method is based on a Riemannian generalization of a cautious update and a weak line search condition. It is shown that, the Riemannian BFGS method converges (i) globally to a stationary point without assuming that the objective function is convex and (ii) superlinearly to a nondegenerate minimizer. The weak line search condition removes completely the need to consider the differentiated retraction. The joint diagonalization problem is used to demonstrate the performance of the algorithm with various parameters, line search conditions, and pairs of retraction and vector transport. |
Year | DOI | Venue |
|---|---|---|
2015 | 10.1007/978-3-319-39929-4_60 | Lecture Notes in Computational Science and Engineering |
Field | DocType | Volume |
Applied mathematics,Computer science,Riemannian manifold,Degeneracy (mathematics),Regular polygon,Theoretical computer science,Stationary point,Line search,Smoothness,Broyden–Fletcher–Goldfarb–Shanno algorithm,Optimization problem,Distributed computing | Conference | 112 |
ISSN | Citations | PageRank |
1439-7358 | 0 | 0.34 |
References | Authors | |
0 | 3 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Wen Huang | 1 | 77 | 8.07 |
| Pierre-Antoine Absil | 2 | 348 | 34.17 |
| Kyle Gallivan | 3 | 889 | 154.22 |