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.