Name
Abstract | ||
|---|---|---|
Saddle-point systems arise in many applications areas, in fact in any situation where an extremum principle arises with constraints. The Stokes problem describing slow viscous flow of an incompressible fluid is a classic example coming from PDEs and in the area of optimization such problems are ubiquitous. In this paper we present a framework into which many well-known methods for solving saddle-point systems fit. Based on this description we show how new approaches for the solution of saddle-point systems arising in optimization can be derived from the Bramble-Pasciak conjugate gradient approach widely used in PDEs and more recent generalizations thereof. In particular we derive a class of new solution methods based on the use of preconditioned conjugate gradients in nonstandard inner products and demonstrate how these can be understood through more standard machinery. We show connections to constraint preconditioning and give the results of numerical computations on a number of standard optimization test examples. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1137/080727129 | SIAM J. Scientific Computing |
Keywords | Field | DocType |
new solution method,preconditioning saddle-point systems,applications area,bramble-pasciak conjugate gradient approach,preconditioned conjugate gradient,standard optimization test example,saddle-point system,standard machinery,new approach,classic example,stokes problem,preconditioning,saddle point,optimization | Conjugate gradient method,Saddle,Mathematical optimization,Saddle point,Iterative method,Calculus of variations,Incompressible flow,Numerical analysis,Partial differential equation,Mathematics | Journal |
Volume | Issue | ISSN |
32 | 1 | 1064-8275 |
Citations | PageRank | References |
11 | 0.70 | 16 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| H. Sue Dollar | 1 | 98 | 5.43 |
| Nicholas I. M. Gould | 2 | 1445 | 123.86 |
| Martin Stoll | 3 | 197 | 17.97 |
| Andrew J. Wathen | 4 | 796 | 65.47 |