Approximating Hessians in unconstrained optimization arising from discretized problems

Authors:
Vincent Malmedy;Philippe L. Toint
Affiliations:
Fonds de la Recherche Scientifique (FNRS), Bruxelles, Belgium 1000 and Department of Mathematics, University of Namur (FUNDP), Namur, Belgium 5000;Department of Mathematics, University of Namur (FUNDP), Namur, Belgium 5000
Venue:
Computational Optimization and Applications
Year:
2011

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Abstract

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).