A Derivative-Free Optimization Algorithm Combining Line-Search and Trust-Region Techniques

The speeding-up and slowing-down (SUSD) direction is a novel direction, which is proved to converge to the gradient descent direction under some conditions. The authors propose the derivative-free optimization algorithm SUSD-TR, which combines the SUSD direction based on the covariance matrix of interpolation points and the solution of the trust-region subproblem of the interpolation model function at the current iteration step. They analyze the optimization dynamics and convergence of the algorithm SUSD-TR. Details of the trial step and structure step are given. Numerical results show their algorithm's efficiency, and the comparison indicates that SUSD-TR greatly improves the method's performance based on the method that only goes along the SUSD direction. Their algorithm is competitive with state-of-the-art mathematical derivative-free optimization algorithms.