Two modified adaptive cubic regularization algorithms by using the nonmonotone Armijo-type line search

The current study provides two modified adaptive cubic regularized methods for the unconstrained optimization problems. The basis of these methods are based on a combination of the adaptive cubic regularized method (ARC) with the nonmonotone Armijo-type line search. The step lengths are calculated in different paths for the modified algorithms. Moreover, we analyse the global convergence properties for the proposed methods. The obtained results illustrate the capability of the modified algorithms compared to the other provided algorithms.

Automated summary

The current study introduces two modified adaptive cubic regularized (ARC) methods for solving unconstrained optimization problems. These methods combine ARC with the nonmonotone Armijo-type line search and calculate step lengths in different paths. The global convergence properties of the proposed methods are analyzed, and the results demonstrate their superior performance compared to other existing algorithms.