A derivative-free modified tensor method with curvilinear linesearch for unconstrained nonlinear programming

In this paper, a random derivative-free modified tensor method with curvilinear linesearch technique is considered for solving nonlinear programming problems. The proposed algorithm is designed to build polynomial interpolation models for the objective function and build the tensor model using the information of the interpolation function. At the same time, we give a new curvilinear tensor step which guarantees the monotonic decrease on the tensor model. The modified tensor step also asymptotically approaches the modified Newton direction as the step length shrinks to zero, and the objective function of problem will be descendent. Under general assumptions, we give the global and local superlinear convergence of the algorithm. Numerical results are recorded, and the compare results with a tensor algorithm without curvilinear linesearch technique and Newton algorithm show that our algorithm is more effectiveness.