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.