Name
Abstract | ||
|---|---|---|
We investigate real asymmetric linear systems arising in the search direction generation in a nonsmooth Newton's method. This applies to constrained optimisation problems via reformulation of the necessary conditions into an equivalent nonlinear and nonsmooth system of equations. We propose a strategy to exploit the problem structure. First, based on the sub-blocks of the original matrix, some variables are selected and ruled out for a posteriori recovering; then, a smaller and symmetric linear system is generated; eventually, from the solution of the latter, the remaining variables are obtained. We prove the method is applicable if the original linear system is well-posed. We propose and discuss different selection strategies. Finally, numerical examples are presented to compare this method with the direct approach without exploitation, for full and sparse matrices, in a wide range of problem size. |
Year | DOI | Venue |
|---|---|---|
2019 | 10.1007/978-3-030-22744-9_32 | COMPUTATIONAL SCIENCE - ICCS 2019, PT III |
Keywords | Field | DocType |
Structure exploitation, Linear algebra, Nonsmooth Newton's method, Nonlinear optimization | Linear algebra,Mathematical optimization,Nonlinear system,System of linear equations,Linear system,Computer science,Matrix (mathematics),Nonlinear programming,Sparse matrix,Newton's method | Conference |
Volume | ISSN | Citations |
11538 | 0302-9743 | 0 |
PageRank | References | Authors |
0.34 | 0 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Alberto De Marchi | 1 | 0 | 0.34 |
| M. Gerdts | 2 | 58 | 11.18 |