Projector preconditioning for partially bound-constrained quadratic optimization

Abstract

Preconditioning by a conjugate projector is combined with the recently proposed modified proportioning with reduced gradient projection (MPRGP) algorithm for the solution of bound-constrained quadratic programming problems. If applied to the partially bound-constrained problems, such as those arising from the application of FETI-based domain decomposition methods to the discretized elliptic boundary variational inequalities, the resulting algorithm is shown to have better bound on the rate of convergence than the original MPRGP algorithm. The performance of the algorithm is illustrated on the solution of a model boundary variational inequality.