Alternating direction method for a class of bilinear programming problem with its applications

In this paper, we design a novel alternating update method for solving a class of generalized bilinear programming problem, where each subproblem is regularized by a positive-definite proximal term to guarantee the convergence of the method. By using the tool of the variational inequality and the property of a monotonicity operator, its global convergence is analyzed and a worst-case O(1/t) convergence rate in an ergodic sense is established. In order to accelerate the convergence of the proposed method, we also introduce a linearized strategy to approximately deal with the involved subproblems. Several numerical examples are tested to verify the feasibility and efficiency of the proposed method.