An algorithm for solving the general linear programming problem

The paper proposes an algorithm, called SGGP, for solving a general linear programming problem. The proposed algorithm works directly in the primal variables space and comprises two phases. Phase I (initialization of the algorithm or determination of an extreme point of a convex polyhedron, which uses phase II as in the Simplex Algorithm) has been constructed in two forms (primal and dual procedures). Designed as a natural extension of the Simplex Algorithm, the algorithm SGGP contains its usual variants (dual Simplex, case of bounded variables, ...). It is shown that SGGP is a projected gradient method with an extreme point of the convex polyhedron as the starting point.