A nonmonotone line search technique for Newton's method
SIAM Journal on Numerical Analysis
Newton's method for B-differentiable equations
Mathematics of Operations Research
On concepts of directional differentiability
Journal of Optimization Theory and Applications
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
An affine scaling trust-region approach to bound-constrained nonlinear systems
Applied Numerical Mathematics
Journal of Computational and Applied Mathematics
A globally convergent Newton-GMRES method for large sparse systems of nonlinear equations
Applied Numerical Mathematics
Smoothing SQP algorithm for semismooth equations with box constraints
Computational Optimization and Applications
Hi-index | 7.30 |
We develop and analyze a new affine scaling Levenberg-Marquardt method with nonmonotonic interior backtracking line search technique for solving bound-constrained semismooth equations under local error bound conditions. The affine scaling Levenberg-Marquardt equation is based on a minimization of the squared Euclidean norm of linear model adding a quadratic affine scaling matrix to find a solution that belongs to the bounded constraints on variable. The global convergence results are developed in a very general setting of computing trial directions by a semismooth Levenberg-Marquardt method where a backtracking line search technique projects trial steps onto the feasible interior set. We establish that close to the solution set the affine scaling interior Levenberg-Marquardt algorithm is shown to converge locally Q-superlinearly depending on the quality of the semismooth and Levenberg-Marquardt parameter under an error bound assumption that is much weaker than the standard nonsingularity condition, that is, BD-regular condition under nonsmooth case. A nonmonotonic criterion should bring about speed up the convergence progress in the contours of objective function with large curvature.