A long-step feasible predictor–corrector interior-point algorithm for symmetric cone optimization. (4th March 2019)

• Record Type: Journal Article
• Authors: Asadi, S.; Mansouri, H.; Darvay, Zs.; Lesaja, G.; Zangiabadi, M.
• Is Part Of: Optimization methods and software. Volume 34:Number 2(2019)
• Page Start: 336
• Page End: 362
• Publication Date: 2019-03-04
• Subjects: Symmetric cone optimization -- Euclidean Jordan algebra -- large neighbourhood of the central path -- predictor–corrector interior-point algorithm -- Nesterov–Todd directions; 90C51 -- 90C33; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2018.1528248
• Languages: English
• ISSNs: 1055-6788

Abstract

ABSTRACT: In this paper, we present a feasible predictor–corrector interior-point method for symmetric cone optimization problem in the large neighbourhood of the central path. The method is generalization of Ai-Zhang's predictor–corrector algorithm to the symmetric cone optimization problem. Starting with a feasible point( x 0, y 0, s 0 ) in given large neighbourhood of the central path, the algorithm still terminates in at mostO r log ⁡ ( T r ( x 0 ∘ s 0 ) / ε ) iterations. This matches the best known iteration bound that is usually achieved by short-step methods, thereby, closing the complexity gap between long- and short-step interior-point methods for symmetric cone optimization. The preliminary numerical results on a selected set of NETLIB problems show advantage of the method in comparison with the version of the algorithm that is not based on the predictor–corrector scheme.