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-Mendonça (2008).
Technical Report 08/19, Department of Mathematics, University of Namur, Namur, Belgium, November 2008
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