The Accuracy of Interior-Point Methods Based on Kernel Functions

Vieira, Manuel V. C. "The Accuracy of Interior-Point Methods Based on Kernel Functions." J. Optimization Theory and Applications. 155.2 (2012): 637-649.


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.