On the convergence of interiorreflective Newton methods for nonlinear minimization subject to bounds
 Thomas F. Coleman,
 Yuying Li
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We consider a new algorithm, an interiorreflective 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 generatesstrictly feasible iterates by using a new affine scaling transformation and following piecewise linear paths (reflection paths). The interiorreflective approach does not require identification of an “activity set”. In this paper we establish that the interiorreflective Newton approach is globally and quadratically convergent. Moreover, we develop a specific example of interiorreflective Newton methods which can be used for largescale and sparse problems.
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 Title
 On the convergence of interiorreflective Newton methods for nonlinear minimization subject to bounds
 Journal

Mathematical Programming
Volume 67, Issue 13 , pp 189224
 Cover Date
 19941001
 DOI
 10.1007/BF01582221
 Print ISSN
 00255610
 Online ISSN
 14364646
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Box constraints
 Interiorpoint method
 Nonlinear minimization
 Industry Sectors
 Authors

 Thomas F. Coleman ^{(1)}
 Yuying Li ^{(2)}
 Author Affiliations

 1. Computer Science Department, Cornell University, 14853, Ithaca, New York, USA
 2. Center for Applied Mathematics, Cornell University, 14853, Ithaca, New York, USA