Second-Order Convergence Properties of Trust-Region Methods Using Incomplete Curvature Information, with an Application to Multigrid Optimization

Second-Order Convergence Properties of Trust-Region Methods Using Incomplete Curvature Information, with an Application to Multigrid Optimization

Year:    2006

Journal of Computational Mathematics, Vol. 24 (2006), Iss. 6 : pp. 676–692

Abstract

Convergence properties of trust-region methods for unconstrained nonconvex optimization is considered in the case where information on the objective function's local curvature is incomplete, in the sense that it may be restricted to a fixed set of "test directions" and may not be available at every iteration. It is shown that convergence to local "weak" minimizers can still be obtained under some additional but algorithmically realistic conditions. These theoretical results are then applied to recursive multigrid trust-region methods, which suggests a new class of algorithms with guaranteed second-order convergence properties.  

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2006-JCM-8783

Journal of Computational Mathematics, Vol. 24 (2006), Iss. 6 : pp. 676–692

Published online:    2006-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    17

Keywords:    Nonlinear optimization Convergence to local minimizers Multilevel problems.