O(n3) noniterative heuristic algorithm for linear programs with error-free implementation

摘要

We present an O(n3) noniterative heuristic algorithm and describe an implementation of p-adic arithmetic to solve the linear programming problems error-free. An optimality test as well as numerical examples depict the scope of such an algorithm. In the few cases where it did not lead to the optimal solution, it did provide a nonnegative solution of the system Ax=b, which could be used as the basic feasible solution for any one of the widely used simplex methods, say, the revised simplex algorithm without the need to include artificial variables in Ax=b for consistency check. Thus the algorithm could be at least a pre-processor for any simplex algorithm and avoids the enhancement of dimensions of the constraint matrix A and consequent additional space, computational complexities, and errors.