Trust-region quadratic methods for nonlinear systems of mixed equalities and inequalities

Two trust-region methods for systems of mixed nonlinear equalities, general inequalities and simple bounds are proposed. The first method is based on a Gauss–Newton model, the second one is based on a regularized Gauss–Newton model and results to be a Levenberg–Marquardt method. The globalization st...

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Vydáno v:Applied numerical mathematics Ročník 59; číslo 5; s. 859 - 876
Hlavní autoři: Macconi, Maria, Morini, Benedetta, Porcelli, Margherita
Médium: Journal Article
Jazyk:angličtina
Vydáno: Kidlington Elsevier B.V 01.05.2009
Elsevier
Témata:
Bound-constrained optimization
Calculus of variations and optimal control
Error bound
Exact sciences and technology
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Numerical methods in mathematical programming, optimization and calculus of variations
Sciences and techniques of general use
Systems of nonlinear equalities and inequalities
Trust-region methods
Error bound
Systems of nonlinear equalities and inequalities
Trust-region methods
Bound-constrained optimization
Error estimation
Numerical linear algebra
Optimization method
Numerical method
Non linear system
Mixed method
Convergence
Constrained optimization
Numerical analysis
Applied mathematics
Condition number
Mathematical programming
ISSN:0168-9274, 1873-5460
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Shrnutí:Two trust-region methods for systems of mixed nonlinear equalities, general inequalities and simple bounds are proposed. The first method is based on a Gauss–Newton model, the second one is based on a regularized Gauss–Newton model and results to be a Levenberg–Marquardt method. The globalization strategy uses affine scaling matrices arising in bound-constrained optimization. Global convergence results are established and quadratic rate is achieved under an error bound assumption. The numerical efficiency of the new methods is experimentally studied.
ISSN:0168-9274
1873-5460
DOI:10.1016/j.apnum.2008.03.028