A linear-time algorithm for the trust region subproblem based on hidden convexity

Jiulin Wang, Yong Xia

Abstract: We present a linear-time approximation scheme for solving the trust region subproblem (TRS). It employs Nesterov’s accelerated gradient descent algorithm to solve a convex programming reformulation of (TRS). The total time complexity is less than that of the recent linear-time algorithm. The algorithm is further extended to the two-sided trust region subproblem.