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.

翻译：弧搜索内点法是一种通过椭球弧逼近中心路径的内点方法，通常能减少迭代次数。为进一步降低求解线性规划问题的迭代次数与计算耗时，本文提出两种采用Nesterov重启策略的弧搜索内点法——该策略是加速动量梯度法的经典方法。第一种方法在邻域内生成迭代序列，我们证明了该序列收敛至最优解且计算复杂度为多项式时间。第二种方法融合了Mehrotra型内点法的思想以提升数值性能。数值实验表明，第二种方法减少了迭代次数与计算时间。特别地，由于动量项的引入，其平均迭代次数相比现有内点法有所降低。