The Shanno-Toint Procedure for Updating Sparse Symmetric Matrices

Michael .J.D. Powell, Philippe Toint

    Research output: Contribution to journalArticlepeer-review


    Two recent methods (Shanno, 1978; Toint, 1980) for revising estimates of sparse second derivative matrices in quasi-Newton optimization algorithms reduce to variable metric formulae when there are no sparsity conditions. It is proved that these methods are equivalent. Further, some examples are given to show that the procedure may make the second derivative approximations worse when the objective function is quadratic. Therefore the convergence properties of the procedure are sometimes less good than the convergence properties of other published methods for revising sparse second derivative approximations. © 1981, by Academic Press Inc. (London) Limited.
    Original languageEnglish
    Pages (from-to)403-413
    Number of pages11
    JournalIMA Journal of Numerical Analysis
    Publication statusPublished - 1 Oct 1981


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