An Improved Trust-Region Method For The Unconstrained Derivative-free Optimization

A novel algorithm is designed to solve nonlinear unconstrained optimization problems,when the derivatives of the objective function can neither be calculated nor be approximated.For the purpose of reducing the amount of calculation of the objective function, we presentthe hybrid algorithm which combines UOBYQA and Multi-directional search method byreconstructing trust region subprolems.A distinguishing feature of the hybrid algorithm is that it solves the two trust regionsubproblems in the same improved trust region which is fixed by the weight of two descentdirections of a triangular simplex. Not only does the hybrid method improve the classic trustregion based on Multi-directional search method algorithm, but also ensures the adequacy ofthe interpolation equations by maximizing the Lagrange functions in the improved trustregion.The numerical experiment shows that the hybrid method is much more efficient thanUOBYQA and other similar algorithms, also demonstrates practicality.