ON THE CONVERGENCE OF THE EXPONENTIAL MULTIPLIER METHOD FOR CONVEX-PROGRAMMING

In this paper, we analyze the exponential method of multipliers for co nvex constrained minimization problems, which operates like the usual Augmented Lagrangian method, except that it uses an exponential penalt y function in place of the usual quadratic. We also analyze a dual cou nterpart, the entropy minimization algorithm, which operates like the proximal minimization algorithm, except that it uses a logarithmic/ent ropy ''proximal'' term in place of a quadratic. We strengthen substant ially the available convergence results for these methods, and we deri ve the convergence rate of these methods when applied to linear progra ms.