A FILTER ALTERNATING DIRECTION METHOD OF MULTIPLIERS FOR FINDING GLOBAL MINIMUM OF BICONVEX OPTIMIZATION

Biconvex optimization is a class of nonconvex optimization problem with frequent occurring in industrial applications. In this paper, a filter alternating direction method of multipliers is proposed for finding a global minimum of biconvex minimization problem. At each iteration, the proposed method solves two subproblems in an alternative fashion, each subproblem minimizes an augmented Lagrangian function restricted to a subset which is determined by the current objective function value. The proposed method can be partly viewed as a Branch and Bound method making use of the biconvexity, it also owns the classical scheme of alternating direction method of multipliers. Some features make it more practical comparing with the existing Branch and Bound methods. The convergence to global minimum has been proved under some suitable assumptions, particularly under the robustness assumption. Some preliminary numerical results indicate that the proposed method is effective.