An exterior point linear programming method based on inclusive nornal cone
journal contribution
posted on 2024-11-01, 08:21authored byYanqun Liu
In this paper, we present a geometrical exterior climbing method based on inclusive normal cones for solving general linear programming prob- lems in canonical form. The method iteratively updates the inclusive cone by climbing within its associated inclusive region (also called a ladder), and even- tually reaches an optimal solution. This method allows the development of a class of `ladder algorithms¿ by using different climbing schemes. Some aspects of the current method are intrinsically related to the dual simplex method. However, it originates from different ideas and provides a new angle to look at the linear programming problem. It can be shown that the dual simplex algo- rithms are special ladder algorithms in this context. We present two climbing schemes leading to two finitely convergent ladder algorithms. The algorithms are tested by solving a number of linear programming examples. Some numer- ical results are provided.