Name
Abstract | ||
|---|---|---|
AbstractThe solution of quadratic or locally quadratic extremum problemssubject to linear(ized) constraints gives rise to linear systems insaddle point form. This is true whether in the continuous or the discretesetting, so saddle point systems arising from the discretization ofpartial differential equation problems, such as those describingelectromagnetic problems or incompressible flow, lead to equationswith this structure, as do, for example, interior point methodsand the sequential quadratic programming approach to nonlinear optimization.This survey concerns iterative solution methods for these problemsand, in particular, shows how the problem formulation leads to naturalpreconditioners which guarantee a fast rate of convergence of the relevantiterative methods. These preconditioners are related to the originalextremum problem and their effectiveness---in terms of rapidityof convergence---is established here via a proof of general boundson the eigenvalues of the preconditioned saddle point matrix on whichiteration convergence depends. |
Year | DOI | Venue |
|---|---|---|
2015 | 10.1137/130934921 | Periodicals |
Keywords | Field | DocType |
inf-sup constant,iterative solvers,preconditioning,saddle point problems | Mathematical optimization,Saddle point,Linear system,Iterative method,Mathematical analysis,Nonlinear programming,Equilibrium point,Rate of convergence,Sequential quadratic programming,Interior point method,Mathematics | Journal |
Volume | Issue | ISSN |
57 | 1 | 0036-1445 |
Citations | PageRank | References |
1 | 0.35 | 0 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jennifer Pestana | 1 | 37 | 9.93 |
| Andrew J. Wathen | 2 | 6 | 1.43 |