Thomas F. Coleman

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We consider a new algorithm, an interior-reflective Newton approach, for the problem of minimizing a smooth nonlinear function of many variables, subject to upper and/or lower bounds on some of the variables. This approach generates strictly feasible iterates by using a new affine scaling transformation and following piecewise linear paths (reflection(More)
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(More)
In many nonlinear problems it is necessary to estimate the Jacobian matrix of a nonlinear mapping F. In large-scale problems the Jacobian of F is usually sparse, and then estimation by differences is attractive because the number of differences can be small compared with the dimension of the problem. For example, if the Jacobian matrix is banded, then the(More)
In solving large sparse linear least squares problems <italic>A</italic> x &sime; b, several different numeric methods involve computing the same upper triangular factor <italic>R</italic> of <italic>A</italic>. It is of interest to be able to compute the nonzero structure of <italic>R</italic>, given only the structure of <italic>A</italic>. The solution(More)