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

Content Provider	Springer Nature Link
Author	Abdi, Fatemeh Shakeri, Fatemeh
Copyright Year	2017
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.
Ending Page	940
Page Count	18
Starting Page	923
File Format	PDF
ISSN	00223239
e-ISSN	15732878
Journal	Journal of Optimization Theory and Applications
Issue Number	3
Volume Number	173
Language	English
Publisher	Springer US
Publisher Date	2017-03-20
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Eigenvalue complementarity problem Josephy–Newton method Gauss–Newton method Complementarity problem Theory of Computation Complementarity and equilibrium problems and variational inequalities (finite dimensions) Optimization Engineering Methods of quasi-Newton type Variational inequality BFGS secant update formula Calculus of Variations and Optimal Control; Optimization Newton-type methods Eigenvalues, eigenvectors Applications of Mathematics Operation Research/Decision Theory Inverse eigenvalue problems
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Control and Optimization Management Science and Operations Research

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