Solution of boolean quadratic programming problems by two augmented Lagrangian algorithms based on a continuous relaxation

Many combinatorial optimization problems and engineering problems can be modeled as boolean quadratic programming (BQP) problems. In this paper, two augmented Lagrangian methods (ALM) are discussed for the solution of BQP problems based on a class of continuous functions. After convexification, the BQP is reformulated as an equivalent augmented Lagrangian function, and then solved by two ALM algorithms. Within this ALM algorithm, L-BFGS is called for the solution of unconstrained nonlinear programming problem. Experiments are performed on max-cut problem, 0-1 quadratic knapsack problem and image deconvolution, which indicate that ALM method is promising for solving large scale BQP by the quality of near optimal solution with low computational time.