Interior-Point Algorithms for Semidefinite Programming Based on A Nonlinear Programming Formulation

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dc.contributor.authorBurer, Samuel
dc.contributor.authorMonteiro, Renato D.C.
dc.contributor.authorZhang, Yin
dc.date.accessioned2018-06-18T17:47:34Z
dc.date.available2018-06-18T17:47:34Z
dc.date.issued1999-12
dc.date.noteDecember 1999
dc.description.abstractRecently, the authors of this paper introduced a nonlinear transformation to convert the positive definiteness constraint on an n × n matrix function of a certain form into the positivity constraint on n scalar variables while keeping the number of variables unchanged. Based on this transformation, they proposed interior point algorithms for solving a special class of linear semidefinite programs. In this paper, we extend this approach and apply the transformation to general linear semidefinite programs, producing nonlinear programs that have not only the n positivity constraints, but also n additional nonlinear inequality constraints. Despite this complication, the transformed problems still retain most of the desirable properties. We propose interior-point algorithms for this type of nonlinear program and establish their global convergence.
dc.format.extent26 pp
dc.identifier.citationBurer, Samuel, Monteiro, Renato D.C. and Zhang, Yin. "Interior-Point Algorithms for Semidefinite Programming Based on A Nonlinear Programming Formulation." (1999) <a href="https://hdl.handle.net/1911/101932">https://hdl.handle.net/1911/101932</a>.
dc.identifier.digitalTR99-27
dc.identifier.urihttps://hdl.handle.net/1911/101932
dc.language.isoeng
dc.titleInterior-Point Algorithms for Semidefinite Programming Based on A Nonlinear Programming Formulation
dc.typeTechnical report
dc.type.dcmiText
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