A global Newton method II: Analytic centers

descriptionPublicationkeyboard_double_arrow_right Article 01 Feb 1993 English Publisher:Springer Science and Business Media LLCJournal:Mathematical Programming, volume 62, pages 223-237 (issn: 0025-5610, eissn: 1436-4646,

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Authors: Allen A. Goldstein;

doi: 10.1007/bf01585168

A global Newton method II: Analytic centers

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Abstract

The author modifies the convergence conditions of a ``backtracking'' global Newton method announced in his previous paper [Ser. Discret. Math. Theor. Comput. Sci. 4, 301-307 (1991; Zbl 0753.58004)] making them sharper and easier to apply. A new version of the Kantorovich inequalities is presented that is simple to state and prove. An application is made to the centering problem for polytopes and an algorithm is given for the feasibility problem of linear inequalities.

Related Organizations

University of Washington
United States
University of Mary
United States

Keywords

centering, Analysis of algorithms and problem complexity, analytic centers, global Newton method, Implicit function theorems; global Newton methods on manifolds

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