The optimization of nonlinear 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, three subgradient-based methods, the subgradient (SG), the surrogate subgradient (SSG) and the surrogate modified subgradient (SMSG), are adopted to solve a demonstrative nonlinear programming problem to assess the performances on optimality in order to demonstrate its applicability to the realistic problem.