A Second-Order Algorithm for the Distance Of A Point to An Epigraph

摘要

We proposed a second-order algorithm for the distance of a point to an epigraph in our paper. We transformed the distance into a finite generalized minimax problem and came up with the optimality conditions. A converges Q-superlinearly algorithm had been presented by using optimality functions which is based on second-order approximations of the cost function and corresponding search direction functions. Finally, to verify the effectiveness of the proposed algorithm, the nonsmooth Lyapunov function was utilized to generate nonlinear control system. Simulation results indicate that the rate of convergence is super-linear.