Mathematical Programming

, Volume 67, Issue 1, pp 189–224

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

  • Thomas F. Coleman
  • Yuying Li

DOI: 10.1007/BF01582221

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


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 generatesstrictly 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.


Box constraintsInterior-point methodNonlinear minimization

Copyright information

© The Mathematical Programming Society, Inc 1994

Authors and Affiliations

  • Thomas F. Coleman
    • 1
  • Yuying Li
    • 2
  1. 1.Computer Science DepartmentCornell UniversityIthacaUSA
  2. 2.Center for Applied MathematicsCornell UniversityIthacaUSA