Khalid El Yassini - A two parameter mixed penalty algorithm for linear programming

We describe a primal-dual interior-exterior algorithm for linear programming problem. The algorithm is based on path following idea and uses a two parameter mixed penalty function. Each iteration updates the penalty parameters and finds an approximate solution of Karush-Kuhn-Tucker system of equations which characterizes a solution of the mixed penalty function. The approximate solution obtained gives a dual and a lambda-feasible primal points which converge to dual and primal solutions.