Lagrangian dual function solved with surrogate subgradient method: An analysis of step size rules

Abstract

Lagrangian relaxation dual function is a technique commonly used to optimize non-convex problems. The difficulty in obtaining a solution method for the dual function is normally due to the function’s non-differentiable characteristic. The most common technique used for these cases is the subgradient-based method. A number of modified subgradients techniques were created in the past decade. In this paper an analysis is carried out on one of the modified technique known as the surrogate subgradient technique(SSG). The analysis is done to investigate the effect of four different step size rules onto the convergence of the dual function. Graphical analysis were carried out to validate and illustrate the convergence.