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

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dc.contributor.authorBurer, Samuel
dc.contributor.authorMonteiro, Renato D.C.
dc.contributor.authorZhang, Yin
dc.date.accessioned2018-06-18T17:47:33Z
dc.date.available2018-06-18T17:47:33Z
dc.date.issued1999-09
dc.date.noteSeptember 1999
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.
dc.format.extent29 pp
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>.
dc.identifier.digitalTR99-17
dc.identifier.urihttps://hdl.handle.net/1911/101922
dc.language.isoeng
dc.titleSolving Semidefinite Programs via Nonlinear Programming, Part I: Transformations and Derivatives
dc.typeTechnical report
dc.type.dcmiText
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