Abstract

We give a general description of a new advanced implementation of the simplex method for linear programming. The method "decouples" a notion of the simplex basic solution into two independent entities: a solution and a basis . This generalization makes it possible to incorporate new strategies into the algorithm since the iterates no longer need to be the vertices of the simplex. An advantage of such approach is a possibility of taking steps along directions that are not simplex edges (in principle they can even cross the interior of the feasible set). It is exploited in our new approach to finding the initial solution in which global infeasibility is handled through a dynamically adjusted penalty term. We present several new techniques that have been incorporated into the method. These features include: ffl previously mentioned method for finding an initial solution, ffl an original approximate steepest edge pricing algorithm, ffl dynamic adjustment of the penalty term. The presenc...

Citations