Please use this identifier to cite or link to this item: https://doi.org/10.1137/S1052623400370503
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dc.titleA multiple-cut analytic center cutting plane method for semidefinite feasibility problems
dc.contributor.authorToh, K.-C.
dc.contributor.authorZhao, G.
dc.contributor.authorSun, J.
dc.date.accessioned2013-10-09T06:18:29Z
dc.date.available2013-10-09T06:18:29Z
dc.date.issued2002
dc.identifier.citationToh, K.-C., Zhao, G., Sun, J. (2002). A multiple-cut analytic center cutting plane method for semidefinite feasibility problems. SIAM Journal on Optimization 12 (4) : 1126-1146. ScholarBank@NUS Repository. https://doi.org/10.1137/S1052623400370503
dc.identifier.issn10526234
dc.identifier.urihttp://scholarbank.nus.edu.sg/handle/10635/44200
dc.description.abstractWe consider the problem of finding a point in a nonempty bounded convex body F in the cone of symmetric positive semidefinite matrices S+ m. Assume that Γ is defined by a separating oracle, which, for any given m × m symmetric matrix Ŷ, either confirms that Ŷ ∈ Γ or returns several selected cuts, i.e., a number of symmetric matrices Ai, i = 1,...,p, p ≤ pmax, such that Γ is in the polyhedron {Y ∈ S+ m | Ai • Y ≤ Ai • Ŷ, i = 1, ⋯,p}. We present a multiple-cut analytic center cutting plane algorithm. Starting from a trivial initial point, the algorithm generates a sequence of positive definite matrices which are approximate analytic centers of a shrinking polytope in S+ m. The algorithm terminates with a point in F within O(m3pmax/ε2) Newton steps (to leading order), where e is the maximum radius of a ball contained in Γ.
dc.description.urihttp://libproxy1.nus.edu.sg/login?url=http://dx.doi.org/10.1137/S1052623400370503
dc.sourceScopus
dc.subjectAnalytic center
dc.subjectCutting plane methods
dc.subjectMultiple cuts
dc.subjectSemidefinite programming
dc.typeArticle
dc.contributor.departmentDECISION SCIENCES
dc.contributor.departmentMATHEMATICS
dc.description.doi10.1137/S1052623400370503
dc.description.sourcetitleSIAM Journal on Optimization
dc.description.volume12
dc.description.issue4
dc.description.page1126-1146
dc.identifier.isiut000175810600014
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