# On the convergence of interior-reflective Newton methods for nonlinear minimization subject to bounds

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DOI: 10.1007/BF01582221

- Cite this article as:
- Coleman, T.F. & Li, Y. Mathematical Programming (1994) 67: 189. doi:10.1007/BF01582221

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## Abstract

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 paths*). The interior-reflective approach does not require identification of an “activity set”. In this paper we establish that the interior-reflective Newton approach is globally and quadratically convergent. Moreover, we develop a specific example of interior-reflective Newton methods which can be used for large-scale and sparse problems.