Preconditioned ADMM for a Class of Bilinear Programming Problems

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 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.

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