New starting point in IPM for SP

Abstract

 In this article we will give a new starting point for interior points method to solve multi stage stochastic programming problems. In the past, several other ways were used to solve such that problems like Bender's decomposition. Many researchers have suggested the use of interior points method to solve the programs arising from stochastic problems because that the programs resulting from stochastic problems have become huge. Interior points is used to solve this problem, the idea was to take a discounted events tree from a basic tree and solved it then take the solution as an initial point to whole problem. Since choosing the starting point to the interior points method of the studied problem plays an important role to speed the convergence of this method. So in this article, we will introduce a new technique to give starting point to the interior points method. We will rely on the scenarios solution, scenario after another taking the solution of the previous stage and use it as a starting point in the current problem. In the following sections we will mention a brief overview of the stochastic programming and interior points method and then recall some elementary points to some researchers, and then we will submit the point that we proposing.