An affine scaling interior-point adaptive cubic regularization algorithm with line search filter technique for derivative-free nonlinear optimization subject to bounds

In this paper, we propose an adaptive cubic regularization method with line search filter tech-nique for solving derivative-free bound constrained optimization using an interior affine scaling approach. The affine scaling interior-point cubic model is based on the quadratic interpolation model of the objective function. The new iteration is obtained by solving the adaptive cubic regularization algorithm with line search filter technique. The global convergence and local superlinear convergence rate of the proposed algorithm are established under some mild conditions. Finally, the numerical results are detailed to show the effectiveness of the proposed algorithm.