An arc-search interior-point method is a type of interior-point methods that approximate 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 stability. 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 by 6% compared to an existing arc-search interior-point method due to the momentum term.

翻译：弧搜索内点法是一类通过椭圆弧逼近中心路径的内点方法，通常能减少迭代次数。为进一步减少求解线性规划问题的迭代次数和计算时间，本文提出了两种采用Nesterov重启策略（一种通过动量项加速梯度法的经典方法）的弧搜索内点法。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于最优解，且计算复杂度为多项式时间。第二种方法结合了Mehrotra型内点法的思想以提升数值稳定性。数值实验表明，第二种方法有效减少了迭代次数和计算时间。特别地，由于引入动量项，其平均迭代次数较现有弧搜索内点法降低了6%。