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Scalar Correction Method for Solving Large Scale Unconstrained Minimization Problems

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Abstract

We introduce a gradient descent algorithm for solving large scale unconstrained nonlinear optimization problems. The computation of the initial trial steplength is based on the usage of both the quasi-Newton property and the Hessian inverse approximation by an appropriate scalar matrix. The nonmonotone line search technique for the steplength calculation is applied later. The computational and storage complexity of the new method is equal to the computational and storage complexity of the Barzilai and Borwein method. On the other hand, the reported numerical results indicate improvements in favor of the new method with respect to the well known global Barzilai and Borwein method.

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Authors and Affiliations

  1. Faculty of Sciences and Mathematics, University of Niš, Višegradska 33, 18000, Niš, Serbia

    Marko Miladinović, Predrag Stanimirović & Sladjana Miljković

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  1. Marko Miladinović
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  2. Predrag Stanimirović
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  3. Sladjana Miljković
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Correspondence to Marko Miladinović.

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Miladinović, M., Stanimirović, P. & Miljković, S. Scalar Correction Method for Solving Large Scale Unconstrained Minimization Problems. J Optim Theory Appl 151, 304–320 (2011). https://doi.org/10.1007/s10957-011-9864-9

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  • DOI: https://doi.org/10.1007/s10957-011-9864-9

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