Name
Title | ||
|---|---|---|
On R-linear convergence of semi-monotonic inexact augmented Lagrangians for saddle point problems. |
Abstract | ||
|---|---|---|
A variant of the inexact augmented Lagrangian algorithm called SMALE (Dostál in Comput. Optim. Appl. 38:47–59, ) for the solution of saddle point problems with a positive definite left upper block is studied. The algorithm SMALE-M presented here uses a fixed regularization parameter and controls the precision of the solution of auxiliary unconstrained problems by a multiple of the norm of the residual of the second block equation and a constant which is updated in order to enforce increase of the Lagrangian function. A nice feature of SMALE-M inherited from SMALE is its capability to find an approximate solution in a number of iterations that is bounded in terms of the extreme eigenvalues of the left upper block and does not depend on the off-diagonal blocks. Here we prove the R-linear rate of convergence of the outer loop of SMALE-M for any regularization parameter. The theory is illustrated by numerical experiments. |
Year | DOI | Venue |
|---|---|---|
2014 | 10.1007/s10589-013-9611-2 | Comp. Opt. and Appl. |
Keywords | Field | DocType |
Quadratic programming,Equality constraints,Augmented Lagrangians,Adaptive precision control,Error bounds,Periodic boundary conditions | Monotonic function,Mathematical optimization,Saddle point,Mathematical analysis,Regularization (mathematics),Augmented Lagrangian method,Rate of convergence,Quadratic programming,Eigenvalues and eigenvectors,Mathematics,Bounded function | Journal |
Volume | Issue | ISSN |
58 | 1 | 0926-6003 |
Citations | PageRank | References |
2 | 0.41 | 3 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Zdenek Dostál | 1 | 53 | 8.03 |
| David Horák | 2 | 35 | 6.79 |
| Petr Vodstrčil | 3 | 8 | 1.60 |