Newton's method for B-differentiable equations
Mathematics of Operations Research
Exponential nonnegativity on the ice cream cone
SIAM Journal on Matrix Analysis and Applications
A nonsmooth version of Newton's method
Mathematical Programming: Series A and B
Growth behavior of a class of merit functions for the nonlinear complementarity problem
Journal of Optimization Theory and Applications
A New Class of Semismooth Newton-Type Methods for Nonlinear Complementarity Problems
Computational Optimization and Applications
Smoothing Functions for Second-Order-Cone Complementarity Problems
SIAM Journal on Optimization
Nonsmooth Equations in Optimization: Regularity, Calculus, Methods and Applications (Nonconvex Optimization and Its Applications)
The eigenvalue complementarity problem
Computational Optimization and Applications
A family of NCP functions and a descent method for the nonlinear complementarity problem
Computational Optimization and Applications
Local minima of quadratic forms on convex cones
Journal of Global Optimization
Cone-constrained eigenvalue problems: theory and algorithms
Computational Optimization and Applications
Reconstructing a matrix from a partial sampling of Pareto eigenvalues
Computational Optimization and Applications
A new method for solving Pareto eigenvalue complementarity problems
Computational Optimization and Applications
Equilibrium problems involving the Lorentz cone
Journal of Global Optimization
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We study several variants of a nonsmooth Newton-type algorithm for solving an eigenvalue problem of the form $$K\ni x\perp(Ax-\lambda Bx)\in K^{+}.$$ Such an eigenvalue problem arises in mechanics and in other areas of applied mathematics. The symbol K refers to a closed convex cone in the Euclidean space 驴 n and (A,B) is a pair of possibly asymmetric matrices of order n. Special attention is paid to the case in which K is the nonnegative orthant of 驴 n . The more general case of a possibly unpointed polyhedral convex cone is also discussed in detail.