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On the convergence of interior-reflective Newton methods for nonlinear minimization subject to bounds
Authors:Thomas F Coleman  Yuying Li
Institution:(1) Computer Science Department, Cornell University, 14853 Ithaca, New York, USA;(2) Center for Applied Mathematics, Cornell University, 14853 Ithaca, New York, USA
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 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 ldquoactivity setrdquo. 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.Research partially supported by the Applied Mathematical Sciences Research Program (KC-04-02) of the Office of Energy Research of the U.S. Department of Energy under grant DE-FG02-86ER25013.A000, and in part by NSF, AFOSR, and ONR through grant DMS-8920550, and by the Advanced Computing Research Institute, a unit of the Cornell Theory Center which receives major funding from the National Science Foundation and IBM Corporation, with additional support from New York State and members of its Corporate Research Institute.Corresponding author.
Keywords:Box constraints  Interior-point method  Nonlinear minimization
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