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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

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 = {Serge Gratton, Annick Sartenaer and Philippe L. Toint}, 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 AU - Serge Gratton, Annick Sartenaer & Philippe L. Toint 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, Convergence to local minimizers, 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 and Philippe L. Toint. (2006). 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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