An augmented Lagrangian method for binary quadratic programming based on a class of continuous functions

In this paper, an augmented Lagrangian method is proposed for binary quadratic programming (BQP) problems based on a class of continuous functions. The binary constraints are converted into a class of continuous functions. The approach reformulates the BQP problem as an equivalent augmented Lagrangian function, and then seeks its minimizer via an augmented Lagrangian method, in which the subproblem is solved by Barzilai–Borwein type method. Numerical results are reported for max-cut problem. The results indicate that the augmented Lagrangian approach is promising for large scale binary quadratic programming by the quality of the near optimal values and the low computational time.