A wide neighbourhood predictor-corrector infeasible-interior-point algorithm for symmetric cone programming

• Published in: Optimization methods & software Vol. 37; no. 6; pp. 2103 - 2120
• Main Authors: Shahraki, M. Sayadi, Mansouri, H., Delavarkhalafi, A.
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 02.11.2022; Taylor & Francis Ltd
• Subjects: Algorithms; Euclidean Jordan algebra; Infeasible-interior-point algorithm; Predictor-corrector methods; symmetric cone programming; wide neighbourhood
• ISSN: 1055-6788; 1029-4937
• DOI: 10.1080/10556788.2022.2060970

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 $ \mathcal {N}_\infty ^- $ N ∞ − , it does not necessarily stay within it but must stay within the wider neighbourhood $ \mathcal {N}(\tau,\, \beta ) $ N ( τ , β ) . We prove that, besides the predictor step, each corrector step also reduces the duality gap by a rate of $ 1-\frac {1}{{O}\left (\sqrt {r}\right )} $ 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.