Preconditioned ADMM for a Class of Bilinear Programming Problems

Abstract EN

We design a novel preconditioned alternating direction method for solving a class of bilinear programming problems, where each subproblem is solved by adding a positive-definite regularization term with a proximal parameter.

By the aid of the variational inequality, the global convergence of the proposed method is analyzed and a worst-case O(1/t) convergence rate in an ergodic sense is established.

Several preliminary numerical examples, including the Markowitz portfolio optimization problem, are also tested to verify the performance of the proposed method.