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.