A boundedness property of the Jacobian matrix arising in regularized interior-point methods

Abstract : We present a uniform boundedness property of a sequence of in- verses of Jacobian matrices that arises in regularized primal-dual interior-point methods in linear and nonlinear programming. We then show how this new result can be applied to the analysis of the global convergence properties of these methods. In particular, we will detail the convergence analysis of an interior point method to solve nonlinear optimization problems, with dynamic updates of the barrier parameter.