| SECOND-ORDER CONVERGENCE PROPERTIES OF TRUST-REGION METHODS USING INCOMPLETE CURVATURE INFORMATION, WITH AN APPLICATION TO MULTIGRID OPTIMIZATION |
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| 引用本文： | Serge Gratton Annick Sartenaer Philippe L. Toint. SECOND-ORDER CONVERGENCE PROPERTIES OF TRUST-REGION METHODS USING INCOMPLETE CURVATURE INFORMATION, WITH AN APPLICATION TO MULTIGRID OPTIMIZATION[J]. 计算数学(英文版), 2006, 24(6): 676-692 |
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| 作者姓名： | Serge Gratton Annick Sartenaer Philippe L. Toint |
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| 作者单位： | Department of Mathematics University of Namur，61，rue de Bruxelles，B-5000 Namur，Belgium，Department of Mathematics，University of Namur，61，rue de Bruxelles，B-5000 Namur，Belgium |
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| 摘 要： | Convergence properties of trust-region methods for unconstrained nonconvex optimiza-tion is considered in the case where information on the objective function's local curvatureis 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 condi-tions.These theoretical results are then applied to recursive multigrid trust-region meth-ods,which suggests a new class of algorithms with guaranteed second-order convergenceproperties.
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| 关 键 词： | 非线性优化 控制论 数学理论 规划论 最优控制 |
| 收稿时间： | 2005-11-07 |
| 修稿时间： | 2005-11-07 |
SECOND-ORDER CONVERGENCE PROPERTIES OF TRUST-REGION METHODS USING INCOMPLETE CURVATURE INFORMATION, WITH AN APPLICATION TO MULTIGRID OPTIMIZATION |
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| Serge Gratton. SECOND-ORDER CONVERGENCE PROPERTIES OF TRUST-REGION METHODS USING INCOMPLETE CURVATURE INFORMATION, WITH AN APPLICATION TO MULTIGRID OPTIMIZATION[J]. Journal of Computational Mathematics, 2006, 24(6): 676-692 |
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| Authors: | Serge Gratton |
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| Abstract: | Convergence properties of trust-region methods for unconstrained nonconvex optimiza- tion 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 condi- tions.These theoretical results are then applied to recursive multigrid trust-region meth- ods,which suggests a new class of algorithms with guaranteed second-order convergence properties. |
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| Keywords: | Nonlinear optimization Convergence to local minimizers Multilevel problems |
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