Interior-Point Algorithms for Semidefinite Programming Based on A Nonlinear Programming Formulation
Monteiro, Renato D.C.
Recently, 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.
Citable link to this pagehttps://hdl.handle.net/1911/101932
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