COMBINED PRIMAL-DUAL AND PENALTY METHODS FOR CONVEX PROGRAMMING

A class of combined primal-dual and penalty methods for constrained minimization is proposed and analyzed, which generalizes the method of multipliers. A convergence and rate of convergence analysis is provided for these methods for the case of a convex programming problem. Global convergence is proved in the presence of both exact and inexact unconstrained minimization, and it is shown that the rate of convergence may be linear or superlinear with arbitrary Q-order of convergence depending on the problem at hand and the form of the penalty function employed.