The optimization of mixed integer programming problem by subgradient-based Lagrangian relaxation

Mathematical programming approaches, such as Lagrangian relaxation, have the advantage of computational efficiency when the optimization problems are decomposable. Lagrangian relaxation belongs to a class of primal-dual algorithms. Subgradient-based optimization methods can be used to optimize the dual functions in Lagrangian relaxation. In this paper, the penalty surrogate subgradient (PSS) method is adopted and compared to solve a demonstrative mixed integer programming problem to assess the performances on optimality in order to demonstrate its applicability to the realistic problem.