An affine scaling trust-region algorithm with interior backtracking technique for solving bound-constrained nonlinear systems

In this paper, we propose a new affine scaling trust-region algorithm in association with nonmonotonic interior backtracking line search technique for solving nonlinear equality systems subject to bounds on variables. The trust-region subproblem is defined by minimizing a squared Euclidean norm of l...

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Veröffentlicht in:Journal of computational and applied mathematics Jg. 184; H. 2; S. 343 - 361
1. Verfasser: Zhu, Detong
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Amsterdam Elsevier B.V 15.12.2005
Elsevier
Schlagworte:
Applied sciences
Exact sciences and technology
Interior point
Mathematical programming
Mathematics
Nonlinear equations
Nonmonotone technique
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in mathematical programming
Numerical methods in mathematical programming, optimization and calculus of variations
Operational research and scientific management
Operational research. Management science
Sciences and techniques of general use
Trust region
Nonlinear equations
Nonmonotone technique
Trust region
Interior point
65 K 05
90 C 30
Search strategy
Convergence acceleration
Constraint
Numerical linear algebra
Interior point method
Confidence region
Non linear equation
Backtracking
Numerical analysis
Algorithm performance
65 K 05 Nonmonoione technique
Condition number
Convergence rate
Feasibility
ISSN:0377-0427, 1879-1778
Online-Zugang:Volltext
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Beschreibung
Zusammenfassung:In this paper, we propose a new affine scaling trust-region algorithm in association with nonmonotonic interior backtracking line search technique for solving nonlinear equality systems subject to bounds on variables. The trust-region subproblem is defined by minimizing a squared Euclidean norm of linear model adding the augmented quadratic affine scaling term subject only to an ellipsoidal constraint. By using both trust-region strategy and interior backtracking line search technique, each iterate switches to backtracking step generated by the general trust-region subproblem and satisfies strict interior point feasibility by line search backtracking technique. The global convergence and fast local convergence rate of the proposed algorithm are established under some reasonable conditions. A nonmonotonic criterion should bring about speeding up the convergence progress in some ill-conditioned cases. The results of numerical experiments are reported to show the effectiveness of the proposed algorithm.
Bibliographie:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2005.01.013