A Subspace, Interior, and Conjugate Gradient Method for Large-Scale Bound-Constrained Minimization Problems

A subspace adaptation of the Coleman--Li trust region and interior method is proposed for solving large-scale bound-constrained minimization problems. This method can be implemented with either sparse Cholesky factorization or conjugate gradient computation. Under reasonable conditions the convergence properties of this subspace trust region method are as strong as those of its full-space version.

Computational performance on various large test problems is reported; advantages of our approach are demonstrated. Our experience indicates that our proposed method represents an efficient way to solve large bound-constrained minimization problems.

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