Abstract
We consider a successive projection method for finding a common point in the intersection of closed convex sets with a nonempty interior. We first generalize an iterative projection algorithm known as acceleration method that was introduced earlier in [1] from the case of two closed convex sets to a finite number of closed convex sets, assuming that the intersection set has a nonempty interior. In particular, we establish the convergence of such an algorithm to a common feasible point in the intersection of all the sets. Following this, we establish a geometric rate of convergence for the generalized method when we restrict the convex sets to the class of half-spaces in finite dimensional Euclidean spaces.
| Original language | English (US) |
|---|---|
| Title of host publication | 2016 American Control Conference, ACC 2016 |
| Publisher | Institute of Electrical and Electronics Engineers Inc. |
| Pages | 4422-4427 |
| Number of pages | 6 |
| Volume | 2016-July |
| ISBN (Electronic) | 9781467386821 |
| DOIs | |
| State | Published - Jul 28 2016 |
| Externally published | Yes |
| Event | 2016 American Control Conference, ACC 2016 - Boston, United States Duration: Jul 6 2016 → Jul 8 2016 |
Other
| Other | 2016 American Control Conference, ACC 2016 |
|---|---|
| Country | United States |
| City | Boston |
| Period | 7/6/16 → 7/8/16 |
Keywords
- Acceleration method
- Closed convex sets
- Convergence rate
- Half-spaces
- Successive projection
ASJC Scopus subject areas
- Electrical and Electronic Engineering
Cite this
Etesami, S. R., Nedich, A., & Basar, T. (2016). Generalization of accelerated successive projection method for convex sets intersection problems. In 2016 American Control Conference, ACC 2016 (Vol. 2016-July, pp. 4422-4427). [7525618] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ACC.2016.7525618