Solving Semidefinite Programs via Nonlinear Programming, Part I: Transformations and Derivatives

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dc.contributor.authorBurer, Samuelen_US
dc.contributor.authorMonteiro, Renato D.C.en_US
dc.contributor.authorZhang, Yinen_US
dc.date.accessioned2018-06-18T17:47:33Zen_US
dc.date.available2018-06-18T17:47:33Zen_US
dc.date.issued1999-09en_US
dc.date.noteSeptember 1999en_US
dc.description.abstractIn this paper, we introduce transformations that convert a large class of linear and/or nonlinear semidefinite programming (SDP) problems into nonlinear optimization problems over "orthants" of the form (R^n)++ × R^N, where n is the size of the matrices involved in the problem and N is a nonnegative integer dependent upon the specific problem. For example, in the case of the SDP relaxation of a MAXCUT problem, N is zero and n, the number of variables of the resulting nonlinear optimization problem, is the number of vertices in the underlying graph. The class of transformable problems includes most, if not all, instances of SDP relaxations of combinatorial optimization problems with binary variables, as well as other important SDP problems. We also derive formulas for the first and second derivatives of the objective function of the resulting nonlinear optimization problem, hence enabling the effective application of existing nonlinear optimization techniques to the solution of large-scale SDP problems.en_US
dc.format.extent29 ppen_US
dc.identifier.citationBurer, Samuel, Monteiro, Renato D.C. and Zhang, Yin. "Solving Semidefinite Programs via Nonlinear Programming, Part I: Transformations and Derivatives." (1999) <a href="https://hdl.handle.net/1911/101922">https://hdl.handle.net/1911/101922</a>.en_US
dc.identifier.digitalTR99-17en_US
dc.identifier.urihttps://hdl.handle.net/1911/101922en_US
dc.language.isoengen_US
dc.titleSolving Semidefinite Programs via Nonlinear Programming, Part I: Transformations and Derivativesen_US
dc.typeTechnical reporten_US
dc.type.dcmiTexten_US
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