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Newton-type Methods for Variational Inequalities
1998Josephy’s Newton and quasi-Newton methods are the basic methods for solving variational inequalities (VI). The subproblem needed to solve is a linear variational inequality problem with the same constraint to the original problem. In this paper, we provide such Newton and quasi-Newton methods for solving VI that the subproblem needed to solve is a ...
Jiye Han, Defeng Sun
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A NEW DAMPING RIEMANNIAN NEWTON-TYPE METHOD
2023This work presents a strategy of linesearch to find singularities of vector fields defined on Riemannian manifolds. It is an adapted of the Armijo rule for preventing a step length quite small on the Newton direction, when it exists. Otherwise, it is kept the Armijo rule in a safeguard direction.
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Backward Step Control for Global Newton-Type Methods
SIAM Journal on Numerical Analysis, 2016Summary: We present and analyze a new damping approach called backward step control for the globalization of the convergence of Newton-type methods for the numerical solution of nonlinear root-finding problems. We provide and discuss reasonable assumptions that imply convergence of backward step control on the basis of generalized Newton paths in ...
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Newton-Type Methods in Computational Guidance
Journal of Guidance, Control, and Dynamics, 2019Binfeng Pan, Yangyang Ma, Rui Yan
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