An affine scaling trust-region approach to bound-constrained nonlinear systems
Applied Numerical Mathematics
STRSCNE: A Scaled Trust-Region Solver for Constrained Nonlinear Equations
Computational Optimization and Applications
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
The Lagrangian Globalization Method for Nonsmooth Constrained Equations
Computational Optimization and Applications
A Combined Global & Local Search (CGLS) Approach to Global Optimization
Journal of Global Optimization
Journal of Computational and Applied Mathematics
An interior-point affine-scaling trust-region method for semismooth equations with box constraints
Computational Optimization and Applications
A new nonmonotone line search technique for unconstrained optimization
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Optimization Methods & Software
Solving bound constrained optimization via a new nonmonotone spectral projected gradient method
Applied Numerical Mathematics
Spectral gradient projection method for monotone nonlinear equations with convex constraints
Applied Numerical Mathematics
Journal of Computational and Applied Mathematics
Convergence of an inexact generalized Newton method with a scaled residual control
Computers & Mathematics with Applications
Parallel Two-Grid Semismooth Newton-Krylov-Schwarz Method for Nonlinear Complementarity Problems
Journal of Scientific Computing
Convergence analysis of a proximal Gauss-Newton method
Computational Optimization and Applications
Gradient trust region algorithm with limited memory BFGS update for nonsmooth convex minimization
Computational Optimization and Applications
Smoothing SQP algorithm for semismooth equations with box constraints
Computational Optimization and Applications
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We develop and analyze a class of trust-region methods for bound-constrained semismooth systems of equations. The algorithm is based on a simply constrained differentiable minimization reformulation. Our global convergence results are developed in a very general setting that allows for nonmonotonicity of the function values at subsequent iterates. We propose a way of computing trial steps by a semismooth Newton-like method that is augmented by a projection onto the feasible set. Under a Dennis--Moré-type condition we prove that close to a regular solution the trust-region algorithm turns into this projected Newton method, which is shown to converge locally q-superlinearly or quadratically, respectively, depending on the quality of the approximate subdifferentials used.As an important application we discuss how the developed algorithm can be used to solve nonlinear mixed complementarity problems (MCPs). Hereby, the MCP is converted into a bound-constrained semismooth equation by means of an NCP-function. The efficiency of our algorithm is documented by numerical results for a subset of the MCPLIB problem collection.