On the convergence of the exponential multiplier method for convex programming

In this paper, the authors analyze the exponential method of multipliers for convex constrained minimization problems, which operates like the usual Augmented Lagrangean method, except that it uses an exponential penalty function in place of the usual quadratic. They also analyze a dual counterpart, the entropy minimization algorithm, which operates like the proximal minimization algorithm, except that it uses a logarithmic/entropy ‘proximal’ term in place of a quadratic. The authors strengthen substantially the available convergence results for these methods, and they derive the convergence rate of these methods when applied to linear programs.