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

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 $ \m...

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Published inOptimization methods & software Vol. 37; no. 6; pp. 2103 - 2120
Main Authors Shahraki, M. Sayadi, Mansouri, H., Delavarkhalafi, A.
Format Journal Article
LanguageEnglish
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
Online AccessGet full text
ISSN1055-6788
1029-4937
DOI10.1080/10556788.2022.2060970

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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 $ \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.
AbstractList 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.
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 , it does not necessarily stay within it but must stay within the wider neighbourhood . We prove that, besides the predictor step, each corrector step also reduces the duality gap by a rate of , 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.
Author Shahraki, M. Sayadi
Delavarkhalafi, A.
Mansouri, H.
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Snippet In this paper, we propose a new predictor-corrector infeasible-interior-point algorithm for symmetric cone programming. Each iterate always follows the usual...
In this paper, we propose a new predictor–corrector infeasible-interior-point algorithm for symmetric cone programming. Each iterate always follows the usual...
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SubjectTerms Algorithms
Euclidean Jordan algebra
Infeasible-interior-point algorithm
Predictor-corrector methods
symmetric cone programming
wide neighbourhood
Title A wide neighbourhood predictor-corrector infeasible-interior-point algorithm for symmetric cone programming
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