Volume 24, Issue 6
Second-Order Convergence Properties of Trust-Region Methods Using Incomplete Curvature Information, with an Application to Multigrid Optimization

Serge Gratton, Annick Sartenaer & Philippe L. Toint

DOI:

J. Comp. Math., 24 (2006), pp. 676-692

Published online: 2006-12

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  • 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.

  • Keywords

Nonlinear optimization convergence to local minimizers multilevel problems

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COPYRIGHT: © Global Science Press

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@Article{JCM-24-676, author = {}, title = {Second-Order Convergence Properties of Trust-Region Methods Using Incomplete Curvature Information, with an Application to Multigrid Optimization}, journal = {Journal of Computational Mathematics}, year = {2006}, volume = {24}, number = {6}, pages = {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. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8783.html} }
TY - JOUR T1 - Second-Order Convergence Properties of Trust-Region Methods Using Incomplete Curvature Information, with an Application to Multigrid Optimization JO - Journal of Computational Mathematics VL - 6 SP - 676 EP - 692 PY - 2006 DA - 2006/12 SN - 24 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8783.html KW - Nonlinear optimization KW - convergence to local minimizers KW - multilevel problems AB - 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.
Serge Gratton, Annick Sartenaer & Philippe L. Toint. (1970). Second-Order Convergence Properties of Trust-Region Methods Using Incomplete Curvature Information, with an Application to Multigrid Optimization. Journal of Computational Mathematics. 24 (6). 676-692. doi:
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