Newton's method for B-differentiable equations
Mathematics of Operations Research
Mathematical Programming: Series A and B
A nonsmooth version of Newton's method
Mathematical Programming: Series A and B
Convergence analysis of some algorithms for solving nonsmooth equations
Mathematics of Operations Research
On a multivariate eigenvalue problem, part I: algebraic theory and a power method
SIAM Journal on Scientific Computing
A semismooth equation approach to the solution of nonlinear complementarity problems
Mathematical Programming: Series A and B
New NCP-functions and their properties
Journal of Optimization Theory and Applications
Matrix market: a web resource for test matrix collections
Proceedings of the IFIP TC2/WG2.5 working conference on Quality of numerical software: assessment and enhancement
A New Class of Semismooth Newton-Type Methods for Nonlinear Complementarity Problems
Computational Optimization and Applications
The Quadratic Eigenvalue Problem
SIAM Review
The eigenvalue complementarity problem
Computational Optimization and Applications
On the asymmetric eigenvalue complementarity problem
Optimization Methods & Software - GLOBAL OPTIMIZATION
Cone-constrained eigenvalue problems: theory and algorithms
Computational Optimization and Applications
A nonsmooth algorithm for cone-constrained eigenvalue problems
Computational Optimization and Applications
Semismooth Newton Methods for Variational Inequalities and Constrained Optimization Problems in Function Spaces
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In this paper, we introduce a new method, called the Lattice Projection Method (LPM), for solving eigenvalue complementarity problems. The original problem is reformulated to find the roots of a nonsmooth function. A semismooth Newton type method is then applied to approximate the eigenvalues and eigenvectors of the complementarity problems. The LPM is compared to SNMmin and SNMFB, two methods widely discussed in the literature for solving nonlinear complementarity problems, by using the performance profiles as a comparing tool (Dolan, Moré in Math. Program. 91:201---213, 2002). The performance measures, used to analyze the three solvers on a set of matrices mostly taken from the Matrix Market (Boisvert et al. in The quality of numerical software: assessment and enhancement, pp. 125---137, 1997), are computing time, number of iterations, number of failures and maximum number of solutions found by each solver. The numerical experiments highlight the efficiency of the LPM and show that it is a promising method for solving eigenvalue complementarity problems. Finally, Pareto bi-eigenvalue complementarity problems were solved numerically as an application to confirm the efficiency of our method.