Can I read Cubic Regularized Newton Method for the Saddle Point Models: A Global and Local Convergence Analysis on EtoBox?

Cubic Regularized Newton Method for the Saddle Point Models: A Global and Local Convergence Analysis by Kevin Huang; Junyu Zhang; Shuzhong Zhang is a Engineering article available to read on EtoBox.

What is Cubic Regularized Newton Method for the Saddle Point Models: A Global and Local Convergence Analysis about?

In this paper, we propose a cubic regularized Newton method for solving the convex-concave minimax saddle point problems. At each iteration, a cubic regularized saddle point subproblem is constructed and solved, which provides a search direction for the iterate. With properly chosen stepsizes, the method is shown to converge to the saddle point with global linear and local superlinear convergence rates, if the saddle point function is gradient Lipschitz and strongly-convex-strongly-concave. In the case that the function is merely convex-concave, we propose a homotopy continuation (or path-following) method. Under a Lipschitz-type error bound condition, we present an iteration complexity bound of O (ln (1/ )) to reach an -solution through a homotopy continuation approach, and the iteration complexity bound becomes O (1/ )under a Hölderian-type error bound condition involving a parameter θ (0 < θ < 1).

Who reads Cubic Regularized Newton Method for the Saddle Point Models: A Global and Local Convergence Analysis?

Author

Kevin Huang; Junyu Zhang; Shuzhong Zhang

Publisher

Springer Science and Business Media LLC

Published

2022

Language

EN

Field

Engineering (Physical Sciences)