A new regularized quasi-Newton algorithm for unconstrained optimization

In this paper, we present a new regularized quasi-Newton algorithm for unconstrained optimization. In this algorithm, an adaptive quadratic term is employed to regularize the quasi-Newton model. At each iteration, the trial step is obtained by solving an unconstrained quadratic subproblem. The global convergence and superlinear convergence of the new algorithm are established under reasonable assumptions. The numerical results show that new algorithm is effective.