Matrix-free algorithm for the large-scale constrained trust-region subproblem†

Abstract

A new ‘matrix-free’ algorithm for the solution of linear inequality constrained, large-scale trust-region subproblems is presented. The matrix-free nature of the algorithm eliminates the need for any matrix factorizations and only requires matrix–vector products. Numerical results that demonstrate the viability of the approach are included. †Contribution of the National Institute of Standards and Technology and not subject to copyright in the UnitedStates.