In this paper, we propose an infeasible arc-search interior-point algorithm for solving nonlinear programming problems. Most algorithms based on interior-point methods are categorized as line search since they compute a next iterate on a straight line determined by a search direction which approximates the central path. The proposed arc-search interior-point algorithm uses an arc for the approximation. We discuss convergence properties of the proposed algorithm. We also conduct numerical experiments on the CUTEst benchmark problems and compare the performance of the proposed arc-search algorithm with that of a line-search algorithm. Numerical results indicate that the proposed arc-search algorithm reaches the optimal solution using fewer iterations but longer times than a line-search algorithm. A modification that leads to a faster arc-search algorithm is also discussed.

在本文中，我们提出了解决非线性规划问题的不可行弧搜索内点算法。大多数基于内点方法的算法被归类为线搜索，因为它们在由近似中心路径的搜索方向确定的直线上计算下一个迭代。所提出的弧线搜索内点算法使用弧线作为近似值。我们讨论了所提出算法的收敛性。我们还对CUTEst基准问题进行了数值实验，并将所提出的弧搜索算法与线搜索算法的性能进行了比较。数值结果表明，所提出的弧搜索算法与线性搜索算法相比，迭代次数更少，但迭代时间却更长。