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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.

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