An infeasible interior-point arc-search method with Nesterov’s restarting strategy for linear programming problems
提出两种采用Nesterov重启策略的弧搜索内点法，通过动量项加速线性规划求解，数值实验表明可减少迭代次数和计算时间。
Abstract An arc-search interior-point method is a type of interior-point method 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 the computation time for solving linear programming problems, we propose two arc-search interior-point methods using Nesterov’s restarting strategy which is a 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 proposed method converges to an optimal solution and that it is a polynomial-time method. 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 the computational time compared to existing interior-point methods due to the momentum term.