محسن اسماعیل بیگی

In each iteration of the derivative-free trust-region algorithms, an approximate model of the optimization function is constructed. Radial basis functions are a convenient tool for building the approximate models. Some trust-region algorithms such as ORBIT use radial basis functions as an interpolation tool. Also, this algorithm stores the interpolation points and function values in each iteration. We found that these stored points could be used optimally. In this paper, we propose an improved version of ORBIT. Our new trust-region algorithm sorts the interpolation points and selects 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 our new algorithm with a gradient-free convergence test.