Valkonen, Tuomo 
ORCID: 0000-0001-6683-3572
(2017)
Interior-proximal primal-dual methods.
Applied Analysis and Optimization 3 (2019), 1-28.
![[img]](https://livrepository.liverpool.ac.uk/style/images/fileicons/text.png) |
Text
1706.07067v1.pdf - Submitted version Download (386kB) |
Abstract
We study preconditioned proximal point methods for a class of saddle point problems, where the preconditioner decouples the overall proximal point method into an alternating primal--dual method. This is akin to the Chambolle--Pock method or the ADMM. In our work, we replace the squared distance in the dual step by a barrier function on a symmetric cone, while using a standard (Euclidean) proximal step for the primal variable. We show that under non-degeneracy and simple linear constraints, such a hybrid primal--dual algorithm can achieve linear convergence on originally strongly convex problems involving the second-order cone in their saddle point form. On general symmetric cones, we are only able to show an $O(1/N)$ rate. These results are based on estimates of strong convexity of the barrier function, extended with a penalty to the boundary of the symmetric cone.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | math.OC, math.OC, 90C25, 90C51 |
| Depositing User: | Symplectic Admin |
| Date Deposited: | 30 Jun 2017 09:24 |
| Last Modified: | 19 Jan 2023 07:01 |
| Related URLs: | |
| URI: | https://livrepository.liverpool.ac.uk/id/eprint/3008227 |
Share
Share
