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A predictor-corrector algorithm for semidefinite programming that uses the factor width cone

Kirschner,Felix
; 
de Klerk,Etienne
Abstract
We propose an interior point method (IPM) for solving semidefinite programming problems (SDPs). The standard interior point algorithms used to solve SDPs work in the space of positive semidefinite matrices. Contrary to that the proposed algorithm works in the cone of matrices of constant factor width. We prove global convergence and provide a complexity analysis. Our work is inspired by a series of papers by Ahmadi, Dash, Majumdar and Hall, and builds upon a recent preprint by Roig-Solvas and Sznaier [arXiv:2202.12374, 2022].
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Publisher Copyright: © The Author(s) 2024.
Date
2025-07
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Tilburg University Research Output Collection
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Keywords
Conic optimization, Factor width cone, Interior point methods, Semidefinite programming
Citation
Kirschner, F & de Klerk, E 2025, 'A predictor-corrector algorithm for semidefinite programming that uses the factor width cone', Vietnam Journal of Mathematics, vol. 53, no. 3, pp. 495-515. https://doi.org/10.1007/s10013-023-00666-8
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https://hdl.handle.net/20.500.14602/80036
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info:eu-repo/semantics/openAccess
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