On the componentwise boundedness away from zero of iterates generated by stabilized interior point methods. (1st February 2023)

• Record Type: Journal Article
• Authors: Qiu, Songqiang
• Is Part Of: Optimization. Volume 72:Number 2(2023)
• Page Start: 551
• Page End: 579
• Publication Date: 2023-02-01
• Subjects: Stabilized interior point method -- barrier problem -- boundedness away from zero -- perturbation theory -- eigenvalue estimate; 90C30 -- 90C55 -- 65K05; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2021.1981893
• Languages: English
• ISSNs: 0233-1934

Abstract

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.