| Abstract: | Two new algorithms are presented for solving linear programs which employ the opposite-sign property defined for a set of vectors in m space. The first algorithm begins with a strictly positive feasible solution and purifies it to a basic feasible solution having objective function value no less under maximization. If this solution is not optimal, then it is drawn back into the interior with the same objective function value, and a restart begins. The second algorithm can begin with any arbitrary feasible point. If necessary this point is purified to a basic feasible solution by dual-feasibility–seeking directions. Should dual feasibility be attained, then a duality value interval is available for estimating the unknown objective function value. If at this juncture the working basis is not primal feasible, then further purification steps are taken tending to increase the current objective function value, while simultaneously seeking another dual feasible solution. Both algorithms terminate with an optimal basic solution in a finite number of steps. |
