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A New Descent Method for Symmetric Non-monotone Variational Inequalities with Application to Eigenvalue Complementarity Problems

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Abstract

In this paper, a modified Josephy–Newton direction is presented for solving the symmetric non-monotone variational inequality. The direction is a suitable descent direction for the regularized gap function. In fact, this new descent direction is obtained by developing the Gauss–Newton idea, a well-known method for solving systems of equations, for non-monotone variational inequalities, and is then combined with the Broyden–Fletcher–Goldfarb–Shanno-type secant update formula. Also, when Armijo-type inexact line search is used, global convergence of the proposed method is established for non-monotone problems under some appropriate assumptions. Moreover, the new algorithm is applied to an equivalent non-monotone variational inequality form of the eigenvalue complementarity problem and some other variational inequalities from the literature. Numerical results from a variety of symmetric and asymmetric eigenvalue complementarity problems and the variational inequalities show a good performance of the proposed algorithm with regard to the test problems.

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Authors and Affiliations

  1. Amirkabir University of Technology, Tehran, Iran

    Fatemeh Abdi & Fatemeh Shakeri

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  1. Fatemeh Abdi
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  2. Fatemeh Shakeri
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Correspondence to Fatemeh Shakeri.

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Communicated by Masao Fukushima.

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Abdi, F., Shakeri, F. A New Descent Method for Symmetric Non-monotone Variational Inequalities with Application to Eigenvalue Complementarity Problems. J Optim Theory Appl 173, 923–940 (2017). https://doi.org/10.1007/s10957-017-1100-9

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  • DOI: https://doi.org/10.1007/s10957-017-1100-9

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