Simplex Initialization: A Survey of Techniques and Trends

The simplex method is one of the most fundamental technologies for solving linear programming (LP) problems and has been widely applied to different practical applications. In the past literature, how to improve and accelerate the simplex method has attracted plenty of research. One important way to achieve this goal is to find a better initialization method for the simplex. In this survey, we aim to provide an overview about the initialization methods in the primal and dual simplex, respectively. We also propose several potential future directions about how to improve the existing initialization methods with the help of advanced learning technologies.