ve08
On the unconstrained optimization of partially separable functions We consider the problem of minimizing a smooth objective function f of n real variables. For n>200 we can only hope to locate a local minimum of f within the usual limitations on storage and computing time by using a minimization algorithm that exploits some special structure of f. One such possibility is that the Hessian G(x) of f(x) has clustered eigenvalues at a minimizer x *, in which case conjugate gradient and limited memory variable metric methods were found to work quite well. However, in general, the performance of these methods is rather unpredictable since, except for certain test functions, the eigenvalue structure of G at or near x * is usually not known. Therefore we pursue the traditional approach of approximating f by local quadratic models, which is computationally feasible even for large n if f has a certain separability structure. This structure is always implied by sparsity of G, and depends only on the way in which the components of x enter into f, and not on the numerical values of f or its derivatives.
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References in zbMATH (referenced in 126 articles , 3 standard articles )
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Sorted by year (- Gao, Wenbo; Goldfarb, Donald: Block BFGS methods (2018)
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- Huang, Wen; Gallivan, K.A.; Absil, P.-A.: A Broyden class of quasi-Newton methods for Riemannian optimization (2015)
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- Cartis, Coralia; Gould, Nicholas I.M.; Toint, Philippe L.: On the oracle complexity of first-order and derivative-free algorithms for smooth nonconvex minimization (2012)
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