An interior point algorithm for a non-linear programming problem

In this paper, we develop and analyze a new approach, inspired by interior points and potential function methods, to solve a nonlinear optimization problem under inequality constraints. The potential function we consider involves a parameter p>0. We study the influence of the value of p on asymptotic properties of an algorithmic framework. Actually, we show the surprising result that to obtain a good asymptotic behavior, the only choice is p = q + 1 where q is the number of active constraints at the solution. With this choice, quadratic convergence is obtained.