On the componentwise boundedness away from zero of iterates generated by stabilized interior point methods. (1st February 2023) - Qiu, Songqiang
Abstract : In this study, we are interested in the lower bounds of primal iterates generated in an inner loop of a class of stabilized interior point methods. By using eigenvalue estimates and the perturbation theory of linear systems, we show that for a fixed barrier parameter, the sequence of primal iterates is bounded away from zero. The results are established under some weak assumptions, which are implied by, for example, a second-order sufficient condition. Moreover, our analysis are independent of the choices of merit functions and penalty factors. Preliminary numerical experiments on some degenerate problems conform the results of this paper.