A random search method for extreme point mathematical programming

An extreme point mathematical programming problem is a linear programming problem where an optimal solution must be feasible for a set of constraints and be an extreme point of another set of constraints. Existing techniques for solving this problem are considered unsatisfactory due to computation requirements. In this paper, the authors develop a new technique that uses the ideas of random search, multi-objective programming and the maximum number of vertices for an n-dimensional polyhedron with m facets. The region of search will be reduced after each successful solution. This method has been programmed on a PC.