A relaxed logarithmic barrier method for semidefinite programming

Interior point methods applied to optimization problems have known a remarkable evolution in the last decades. They are used with success in linear, quadratic and semidefinite programming. Among these methods, primal-dual central trajectory methods have a polynomial convergence and are credited of a good numerical behavior. In this paper, we propose a new central trajectory method where a relaxation parameter is introduced in order to give more flexibility to the theoretical and numerical aspects of the perturbed problems and accelerate the convergence of the algorithm. This claim is confirmed by numerical tests showing the good behavior of the algorithm which is proposed in this paper.

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