Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 0842.90106
Coleman, Thomas F.; Li, Yuying
On the convergence of interior-reflective Newton methods for nonlinear minimization subject to bounds. (English)
[J] Math. Program. 67, No.2 (A), 189-224 (1994). ISSN 0025-5610; ISSN 1436-4646/e

The authors analyze a new affine-scaling interior-point method for the minimization of a nonlinear function $f$ subject to simple bounds on the variables. Unlike the Dikin-Karmarker scaling matrix, the scaling matrix $D(x)$ used in this paper is generated using the distance of the iterates to the bounds and the direction of the gradient. Components of the variables are only scaled by the square root of their distance to the bound if the corresponding component of the negative gradient points to that bound. Using this scaling matrix $D(x)$, the first order necessary conditions can be written as $D(x) \nabla f(x) = 0$. Search directions are computed using a modified Newton method applied to $D(x) \nabla f(x) = 0$. To improve global convergence, in particular to avoid short steps generated because some variables may approach the wrong bounds, reflections of the Newton steps at the bounds are used. Global convergence and local $q$-quadratic convergence of this method is proven.
[M.Heinkenschloss (Trier)]

MSC 2000:: *90C30 Nonlinear programming

Keywords: affine-scaling interior-point method; global convergence; local $q$-quadratic convergence

Cited in: Zbl 1234.94055 Zbl 0945.49023

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]