Failure of global convergence for a class of interior point methods for nonlinear programming
The authors consider nonlinear nonconvex optimization problems of the form \[ \min_{x\in\mathbb{R}^n} f(x),\quad c(x)= 0,\quad x_i\geq 0. \] For these problems, they demonstrate that a class of interior point methods is not globally convergent. It is shown that these algorithms produce limit points that are neither feasible nor stationary points.
scientific article; zbMATH DE number 1538619