Global Newton-type methods and semismooth reformulations for NCP
Applied Numerical Mathematics
A generalized Jacobian based Newton method for semismooth block-triangular system of equations
Journal of Computational and Applied Mathematics
Numerical simulation of two-dimensional Bingham fluid flow by semismooth Newton methods
Journal of Computational and Applied Mathematics
A globally and quadratically convergent method for absolute value equations
Computational Optimization and Applications
Convergence of an inexact generalized Newton method with a scaled residual control
Computers & Mathematics with Applications
Computation of generalized differentials in nonlinear complementarity problems
Computational Optimization and Applications
Directional Sparsity in Optimal Control of Partial Differential Equations
SIAM Journal on Control and Optimization
A quasisecant method for solving a system of nonsmooth equations
Computers & Mathematics with Applications
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The paper presents concrete realizations of quasi-Newton methods for solving several standard problems including complementarity problems, special variational inequality problems, and the Karush--Kuhn--Tucker (KKT) system of nonlinear programming. A new approximation idea is introduced in this paper. The Q-superlinear convergence of the Newton method and the quasi-Newton method are established under suitable assumptions, in which the existence of F'(x*) is not assumed. The new algorithms only need to solve a linear equation in each step. For complementarity problems, the QR factorization on the quasi-Newton method is discussed.