Asymptotic Analysis for Penalty and Barrier Methods in Convex and Linear Programming

We consider a wide class of penalty and barrier methods for convex programming which includes a number of specific functions proposed in the literature. We provide a systematic way to generate penalty and barrier functions in this class, and we analyze the existence of primal and dual optimal paths generated by these penalty methods, as well as their convergence to the primal and dual optimal sets. For linear programming we prove that these optimal paths converge to single points.