An Accelerated Regularized Chebyshev–Halley Method for Unconstrained Optimization

Abstract

In machine learning, most models can be transformed into unconstrained optimization problems, so how to solve the unconstrained optimization problem for different objective functions is always a hot issue. In this paper, a class of unconstrained optimization where objection function has [Formula: see text]th-order derivative and Lipschitz continuous simultaneously is studied. To handle such problems, we propose an accelerated regularized Chebyshev–Halley method based on the Accelerated Hybrid Proximal Extragradient (A-HPE) framework. It proves that convergence complexity of the proposed method is [Formula: see text], which is consistent with the lower iteration complexity bound for third-order tensor methods. Numerical experiments on functions in machine learning demonstrate the promising performance of the proposed method.