“…Internal penalty methods, also known as barrier methods, had an explosive development in the last fifteen years, due to the success of interior point methods for linear programming and for linear complementarity problems (see the monographs [10,18,19,25,27,28,33]; see also the extensions to nonlinear programming in [4,9,11,14,15,29]). The first deep study of the path of optimizers, now known as central path, is due to McLinden [21], followed by Bayer and Lagarias [3] and by Megiddo [22], who gave a definitive characterization of the primal-dual central path.…”