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However, even though there is a legitimate necessity to explore these methods in general spaces, there is an absence of infinite-dimensional counterparts for these methods. In this paper, we present decomposition logarithmic-barrier interior-point methods based on unital Jordan\u2013Hilbert algebras for this class of optimization problems in the infinite-dimensional setting. The results show that the iteration complexity of the proposed algorithms is independent on the choice of Hilbert spaces from which the underlying spin factors are formed, and so it coincides with the best-known complexity obtained by such methods for the finite-dimensional setting. We apply our results to an important problem in stochastic control, namely the two-stage stochastic multi-criteria design problem. We show that the corresponding infinite-dimensional system in this case is a matrix differential Ricatti equation plus a finite-dimensional system, and hence, it can be solved efficiently to find the search direction.<\/jats:p>","DOI":"10.1051\/ro\/2023198","type":"journal-article","created":{"date-parts":[[2023,12,22]],"date-time":"2023-12-22T20:07:29Z","timestamp":1703275649000},"page":"1011-1044","source":"Crossref","is-referenced-by-count":0,"title":["Barrier methods based on Jordan\u2013Hilbert algebras for stochastic optimization in spin factors"],"prefix":"10.1051","volume":"58","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1839-8083","authenticated-orcid":false,"given":"Baha","family":"Alzalg","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"250","published-online":{"date-parts":[[2024,3,4]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","first-page":"653","DOI":"10.3934\/dcds.1998.4.653","volume":"4","author":"Lim","year":"1998","journal-title":"Discrete Cont. 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