The Accuracy of Interior‐Point Methods Based on Kernel Functions

For the last decade, interior‐point methods that use barrier functions induced by some real univariate kernel functions have been studied. In these interior‐point methods, the algorithm stops when a solution is found such that it is close (in the barrier function sense) to a point in the central path with the desired accuracy. However, this does not directly imply that the algorithm generates a solution with prescribed accuracy. Until now, this had not been appropriately addressed. In this paper, we analyze the accuracy of the solution produced by the aforementioned algorithm.