On the Redundancy of Hessian Non-Singularity for Linear Convergence Rate of the Newton Method Applied to the Minimization of Convex Functions
Year: 2024
Type: article
Abstract: A new property of convex functions that makes it possible to achieve the linear rate of convergence of the Newton method during the minimization process is established. Namely, it is proved that, even in the case of singularity of the Hessian at the solution, the Newtonian system is solvable in the vicinity of the minimizer; i.e., the gradient of the objective function belongs to the image of the matrix of second derivatives and, therefore, analogs of the Newton method may be used.
Authors: Yu. G. Evtushenko, A. A. Tretyakov
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W4404415887