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Approximating Hessians in multilevel unconstrained optimization

Vincent Malmedy (vincent.malmedy***at***fundp.ac.be)
Philippe L. Toint (philippe.toint***at***fundp.ac.be)

Abstract: We consider Hessian approximation schemes for large-scale multilevel unconstrained optimization problems, which typically present a sparsity and partial separability structure. This allows iterative quasi-Newton methods to solve them despite of their size. Structured finite-difference methods and updating schemes based on the secant equation are presented and compared numerically inside the multilevel trust-region algorithm proposed by Gratton, Mouffe, Toint and Weber-Mendonša (2008).

Keywords: unconstrained optimization, multilevel problems, sparsity, partial separability, numerical experiences

Category 1: Nonlinear Optimization (Unconstrained Optimization )

Category 2: Applications -- Science and Engineering (Optimization of Systems modeled by PDEs )

Citation: Technical Report 08/19, Department of Mathematics, University of Namur, Namur, Belgium, November 2008

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Entry Submitted: 12/01/2008
Entry Accepted: 12/01/2008
Entry Last Modified: 12/01/2008

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