Subspace trust-region methods for large bound-constrained nonlinear equations

Trust-region methods for solving large bound-constrained nonlinear systems are considered. These allow for spherical or elliptical trust regions where the search for an approximate solution is restricted to a low-dimensional space. A general formulation for these methods is introduced and global and superlinear/quadratic convergence is shown under standard assumptions. Viable approaches for implementation in conjunction with Krylov methods are discussed and the practical performance of the resulting algorithms is shown.