Multivariable optimisation techniques have long been used in all fields for improving the design and performance of systems. Yet the number of well known algorithms that can effectively be used under realistic conditions is usually limited due to many practical considerations such as the limit of applicability to certain classes of problems, the time and computational cost of them under conditions of the problem and more importantly, the efficiency of these algorithms under noisy conditions, which is indeed the case in almost all practical problems. Variants of simplex algorithm have been named since 60's as efficient algorithms in noisy situations. However, no theoretical results have been stablished as regards their convergence and computational efficiency. In this report, we have generalized the simplex method and have addressed theoretical aspects concerning the convergence of the algorithm.