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An inexact infeasible arc-search interior-point method for linear optimization (2403.18155v3)

Published 26 Mar 2024 in math.OC, cs.NA, and math.NA

Abstract: Arc-search interior-point methods (IPMs) are a class of IPMs that utilize an ellipsoidal arc to approximate the central path. On the other hand, inexact IPMs solve the linear equation system for the search direction inexactly at each iteration. In this paper, we propose an inexact infeasible arc-search interior-point method. We establish that the proposed method is a polynomial-time algorithm and we show that its iteration complexity is lower than an inexact infeasible line-search IPM. We conducted numerical experiments with benchmark problems from NETLIB. The numerical results demonstrate that the proposed method can reduce the number of iterations and the computation time compared to an existing inexact line-search IPM.

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