A note on the use of vector barrier parameters for interior-point methods

A key feature to ensure desirable convergence properties in an interior-point method is the appropriate choice of an updating rule for the barrier parameter. In this work we analyze and describe updating rules based on the use of a vector of barrier parameters. We show that these updating rules are well defined and satisfy sufficient conditions to ensure convergence to the correct limit points. We also present some numerical results that illustrate the improved performance of these strategies compared to the use of a scalar barrier parameter.