A new trust-region algorithm based on radial basis function interpolation

Optimization using radial basis functions as an interpolation tool in trust-region (ORBIT), is a derivative-free framework based on fully linear models to solve unconstrained local optimization, especially when the function evaluations are computationally expensive. This algorithm stores the interpolation points and function values to using at subsequent iterations. Despite the comparatively advanced management used for interpolation points, we maintain that ORBIT ignores sorting the interpolation points based on the function values. In this paper, we propose an improved version SORT-ORBIT by sorting the interpolation points and selecting a point as the trust-region center in which the objective function reaches its minimum value. Numerical results indicate the efficiency of the improved version compared with the original version. In addition, to estimate high-accuracy solutions, we equip the ORBIT with a new gradient-free convergence test.