A simplex-like method with bisection for linear programming

The simplex method carries out the pivoting operation on a series of the canonical systems. Using an opposite type of canonical system and according pivoting operation, the proposed method also generates a sequence of points, leading to an optimal vertex; however, these points are generally no longer vertices of the underlying polyhedron. Starting with a bracket on the optimal value and at a ‘good’ basis, it proceeds with objective function values under full control, and promisingly reducing computational cost. The method does not introduce artificial variables.