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A Dai-Liao conjugate gradient algorithm with clustering of eigenvalues

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Abstract

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.

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Authors and Affiliations

  1. Research Institute for Informatics, Center for Advanced Modeling and Optimization, 8-10 Averescu Avenue, Bucharest 1, Romania

    Neculai Andrei

  2. Academy of Romanian Scientists, 54 Splaiul Independenţei, Sector 5. Bucharest, Romania

    Neculai Andrei

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  1. Neculai Andrei
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Correspondence to Neculai Andrei.

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Andrei, N. A Dai-Liao conjugate gradient algorithm with clustering of eigenvalues. Numer Algor 77, 1273–1282 (2018). https://doi.org/10.1007/s11075-017-0362-5

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  • DOI: https://doi.org/10.1007/s11075-017-0362-5

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