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Efficient Hierarchical Optimization using an Algebraic Multilevel Approach

Abderrahmane Benzaoui 1 Régis Duvigneau 1
1 OPALE - Optimization and control, numerical algorithms and integration of complex multidiscipline systems governed by PDE
CRISAM - Inria Sophia Antipolis - Méditerranée , JAD - Laboratoire Jean Alexandre Dieudonné : UMR6621
Abstract : This paper presents an efficient method to reduce the optimization cost. In this method, the eigenvectors of the Hessian of the objective function are determined first. Then, the search for the optimum is carried out successively in subspaces defined by these vectors. For this purpose, the Multi-directional-Search Algorithm is used in this study, but any other optimization algorithm can be employed. The method is validated in two test cases: analytical function and shape reconstruction problem. In both cases, this method shows very promising results.
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Submitted on : Monday, June 29, 2009 - 2:28:01 PM
Last modification on : Friday, January 21, 2022 - 11:28:05 AM
Long-term archiving on: : Tuesday, June 15, 2010 - 7:04:03 PM

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Abderrahmane Benzaoui, Régis Duvigneau. Efficient Hierarchical Optimization using an Algebraic Multilevel Approach. [Research Report] RR-6974, INRIA. 2009, pp.31. ⟨inria-00399949⟩

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