Approximating Hessians in unconstrained optimization arising from discretized problems

V. Malmedy, Philippe Toint

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We consider Hessian approximation schemes for large-scale unconstrained optimization in the context of discretized problems. The considered Hessians typically present a nontrivial 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 et al. (IMA J. Numer. Anal. 28(4):827-861, 2008).
Original languageEnglish
Pages (from-to)1-22
Number of pages22
JournalComputational Optimization and Applications
Issue number1
Publication statusPublished - 1 Sep 2011


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