  An arc-search interior-point method is a type of interior-point methods that
approximates the central path by an ellipsoidal arc, and it can often reduce
the number of iterations. In this work, to further reduce the number of
iterations and computation time for solving linear programming problems, we
propose two arc-search interior-point methods using Nesterov's restarting
strategy that is well-known method to accelerate the gradient method with a
momentum term. The first one generates a sequence of iterations in the
neighborhood, and we prove that the convergence of the generated sequence to an
optimal solution and the computation complexity is polynomial time. The second
one incorporates the concept of the Mehrotra-type interior-point method to
improve numerical performance. The numerical experiments demonstrate that the
second one reduced the number of iterations and computational time. In
particular, the average number of iterations was reduced compared to existing
interior-point methods due to the momentum term.
