A wide neighbourhood predictor–corrector infeasible-interior-point algorithm for symmetric cone programming. (2nd November 2022)

• Record Type: Journal Article
• Authors: Shahraki, M. Sayadi; Mansouri, H.; Delavarkhalafi, A.
• Is Part Of: Optimization methods and software. Volume 37:Number 6(2022)
• Page Start: 2117
• Page End: 2134
• Publication Date: 2022-11-02
• Subjects: Infeasible-interior-point algorithm -- wide neighbourhood -- symmetric cone programming -- Euclidean Jordan algebra; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2022.2060970
• Languages: English
• ISSNs: 1055-6788

Abstract

Abstract : In this paper, we propose a new predictor–corrector infeasible-interior-point algorithm for symmetric cone programming. Each iterate always follows the usual wide neighbourhood N ∞ −, it does not necessarily stay within it but must stay within the wider neighbourhood N ( τ, β ) . We prove that, besides the predictor step, each corrector step also reduces the duality gap by a rate of 1 − 1 O ( r ), where r is the rank of the associated Euclidean Jordan algebra. Moreover, we improve the theoretical complexity bound of an infeasible-interior-point method. Some numerical results are provided as well.