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The resulting algorithm can be applied to a variety of optimization problems, including the important class of semidefinite programs with partially separable structure, in a fully distributed fashion without relying on interior-point methods. We derive update equations by applying the Peaceman\u2013Rachford splitting algorithm to the monotonic inclusion related to the lifted dual problem. The cone constraints are implemented by a reflection method in the lifted dual domain where auxiliary variables are reflected with respect to the intersection of the polar cone and a subspace relating the dual and lifted dual domain. Convergence results are provided for both synchronous and stochastic update schemes, and the proposed algorithm is demonstrated through an application to fully distributed sensor localization based on semidefinite programming.<\/jats:p>","DOI":"10.1137\/24m1693581","type":"journal-article","created":{"date-parts":[[2026,2,24]],"date-time":"2026-02-24T08:00:31Z","timestamp":1771920031000},"page":"263-289","source":"Crossref","is-referenced-by-count":1,"title":["Distributed Nonlinear Conic Optimization with Partially Separable Structure"],"prefix":"10.1137","volume":"36","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5998-1550","authenticated-orcid":true,"given":"Richard","family":"Heusdens","sequence":"first","affiliation":[{"name":"Netherlands Defence Academy (NLDA), Den Helder, the Netherlands; Electrical Engineering, Delft University of Technology, Delft, ZH, 2628 CD, the Netherlands."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Guoqiang","family":"Zhang","sequence":"additional","affiliation":[{"name":"Computer Science, University of Exeter, Exeter, EX4 4QF, United Kingdom."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2026,2,24]]},"reference":[{"key":"ref1","unstructured":"J. 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