Projected gradient methods for linearly constrained problems
Mathematical Programming: Series A and B
SIAM Journal on Numerical Analysis
A nonsmooth version of Newton's method
Mathematical Programming: Series A and B
NE/SQP: a robust algorithm for the nonlinear complementarity problem
Mathematical Programming: Series A and B
Implementation of a continuation method for normal maps
Mathematical Programming: Series A and B - Special issue on computational nonsmooth optimization
On unconstrained and constrained stationary points of the implicit Lagrangian
Journal of Optimization Theory and Applications
Global methods for nonlinear complementarity problems
Mathematics of Operations Research
A Potential Reduction Newton Method for Constrained Equations
SIAM Journal on Optimization
A Probability-One Homotopy Algorithm for Nonsmooth Equations and Mixed Complementarity Problems
SIAM Journal on Optimization
Global Optimization Techniques for Mixed Complementarity Problems
Journal of Global Optimization
NCP Functions Applied to Lagrangian Globalization for the Nonlinear Complementarity Problem
Journal of Global Optimization
Lagrangian globalization methods for nonlinear complementarity problems
Journal of Optimization Theory and Applications
An affine scaling trust-region approach to bound-constrained nonlinear systems
Applied Numerical Mathematics
Spectral gradient projection method for monotone nonlinear equations with convex constraints
Applied Numerical Mathematics
An inexact modified subgradient algorithm for nonconvex optimization
Computational Optimization and Applications
A new filled function method for an unconstrained nonlinear equation
Journal of Computational and Applied Mathematics
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The difficulty suffered in optimization-based algorithms for the solution of nonlinear equations lies in that the traditional methods for solving the optimization problem have been mainly concerned with finding a stationary point or a local minimizer of the underlying optimization problem, which is not necessarily a solution of the equations. One method to overcome this difficulty is the Lagrangian globalization (LG for simplicity) method. This paper extends the LG method to nonsmooth equations with bound constraints. The absolute system of equations is introduced. A so-called Projected Generalized-Gradient Direction (PGGD) is constructed and proved to be a descent direction of the reformulated nonsmooth optimization problem. This projected approach keeps the feasibility of the iterates. The convergence of the new algorithm is established by specializing the PGGD. Numerical tests are given.