Iterative Methods for III-Conditioned Linear Systems for Optimization

摘要

Preconditioned conjugate-gradient methods are proposed for solving the ill-211u001econditioned linear systems which arise in penalty and barrier methods for 211u001enonlinear minimization. The preconditioners are chosen so as to isolate the 211u001edominant cause of ill conditioning. The methods are stabilized using a restricted 211u001eform of iterative refinement. Numerical results illustrate the approaches 211u001econsidered.