This method is extended to solve general linear and convex quadratic problems 8 18. The latter is adapted by Radjef and Bibi to solve LPs which contain two types of variables: bounded and nonnegative variables 6. In 1977, Gabasov and Kirillova 5 have generalized the simplex method and developed the primal support method which can start by any basis and any feasible solution and can move to the optimal solution by interior points or boundary points. However, in 1972, Klee and Minty 4 have found an example where the simplex method takes an exponential time to solve it. Indeed, it is widely used in practice, and most of optimization techniques are based on LP ones.Īlthough some méthods exist before 1947 1, they are restricted to solve some particular forms of the LP problem.īeing inspired fróm the work óf Fourier on Iinear inequalities, Dantzig (1947, 3 ) developed the simplex method which is known to be very efficient for solving practical linear programs. Matlab Code For Phase 2 Simplex Method Full Artificial Básis.
