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

Author

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  • Fatemeh Abdi

    (Amirkabir University of Technology)

  • Fatemeh Shakeri

    (Amirkabir University of Technology)

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.

Suggested Citation

  • Fatemeh Abdi & Fatemeh Shakeri, 2017. "A New Descent Method for Symmetric Non-monotone Variational Inequalities with Application to Eigenvalue Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 173(3), pages 923-940, June.
    • Handle: RePEc:spr:joptap:v:173:y:2017:i:3:d:10.1007_s10957-017-1100-9
    DOI: 10.1007/s10957-017-1100-9
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    References listed on IDEAS

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