Journal of Optimization Theory and Applications

, Volume 151, Issue 2, pp 304–320 | Cite as

Scalar Correction Method for Solving Large Scale Unconstrained Minimization Problems

  • Marko Miladinović
  • Predrag Stanimirović
  • Sladjana Miljković


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.


Nonlinear programming Nonmonotone line search BB method Quasi-Newton methods Gradient descent methods Convergence rate 


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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Marko Miladinović
    • 1
  • Predrag Stanimirović
    • 1
  • Sladjana Miljković
    • 1
  1. 1.Faculty of Sciences and MathematicsUniversity of NišNišSerbia

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