A Nonmonotone Adaptive Method for Solving the Unconstrained Optimization Problems

In this paper, we propose a new technique for solving the large scale unconstrained optimization problems. Using a simple cubic regularization in the trust region subproblem, an efficient adaptive nonmonotone scheme is provided. Under some suitable and standard assumptions, we proof the global convergence properties of the new algorithm. Numerical experiments shows the efficiency of the new proposed algorithm.

Keywords:

Trust region methods , Nonmonotone technique Adaptive cubic regularization method Global convergence.