A Nonstandard Simplex Algorithm for Linear Programming

The simplex algorithm travels, on the underlying polyhedron, from vertex to vertex until reaching an optimal vertex. With the same simplex framework, the proposed algorithm generates a series of feasible points (which are not necessarily vertices). In particular, it is exactly an interior point algorithm if the initial point used is interior. Computational experiments show that the algorithm are very efficient, relative to the standard simplex algorithm. It terminates at an approximate optimal vertex, or at an optimal vertex if a simple purification is incorporated.