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

Fatemeh Abdi () and Fatemeh Shakeri ()
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Fatemeh Abdi: Amirkabir University of Technology
Fatemeh Shakeri: Amirkabir University of Technology

Journal of Optimization Theory and Applications, 2017, vol. 173, issue 3, No 11, 923-940

Abstract: 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.

Keywords: Complementarity problem; Variational inequality; Eigenvalue complementarity problem; Gauss–Newton method; Josephy–Newton method; BFGS secant update formula; 65F15; 65F18; 90C33; 90C53; 49M15 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10957-017-1100-9

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