Abstract
Linear programming is the core model of constrained optimization;and the simplex method is one of the most significant method for the routine use of linear programming. It is ideally suited for post-optimality analysis, although with exponential time complexity. An extension of the simplex algorithm is presented in which a sequence of subsidiary linear programming problems is solved until a solution to the original problem is reached. Each successive subsidiary problem is obtained from the previous one by adding one constraint at a time according to a certain cosine heuristic. Preliminary results for small problems are encouraging.