Numerical Algorithms

, Volume 77, Issue 4, pp 1273–1282 | Cite as

A Dai-Liao conjugate gradient algorithm with clustering of eigenvalues

Original Paper


A new value for the parameter in Dai and Liao conjugate gradient algorithm is presented. This is based on the clustering of eigenvalues of the matrix which determine the search direction of this algorithm. This value of the parameter lead us to a variant of the Dai and Liao algorithm which is more efficient and more robust than the variants of the same algorithm based on minimizing the condition number of the matrix associated to the search direction. Global convergence of this variant of the algorithm is briefly discussed.


Unconstrained optimization Conjugate gradient algorithms Eigenvalues clustering Condition number Wolfe conditions Convergence 


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© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Research Institute for InformaticsCenter for Advanced Modeling and OptimizationBucharest 1Romania
  2. 2.Academy of Romanian ScientistsSector 5. BucharestRomania

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