On the componentwise boundedness away from zero of iterates generated by stabilized interior point methods

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.

Keywords:

• Stabilized interior point method
• barrier problem
• boundedness away from zero
• perturbation theory
• eigenvalue estimate

AMS Subject Classifications:

• 90C30
• 90C55
• 65K05

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the Fundamental Research Funds for the Central Universities [2014QNA62]