Study Of The Nonlinear Programming Simplex Method

In the classic methods to solving nonlinear programming unconstrained problem, we must seek the derivatives of the objective function .However, many practical problem of its functions, except for non-smooth or unable to seek derivative .At this time, to give up on seeking a partial derivative of the method, using the direct method .Nonlinear simplex algorithm is a earlier direct method. And in large number of practical problem, nonlinear simplex algorithm is an effective direct search algorithm. Its concept intuitive and the result of the method stability ,therefore it is a widely used method .Thus ,more researchers pay more attention to the study of the nonlinear simplex method .In recent years the nonlinear simplex method increasing maturity ,but its theoretical research is not yet adequate.In this paper, we mainly introduce the nonlinear programming method and conduct in-depth study. In the second part, we first introduce the original structure of the simplex algorithm and MDS algorithm, analysis its advantages and disadvantages .In the third part of the paper, a new modified nonlinear simplex method is offered, through numerous tests function proved the modified nonlinear simplex method allows more broad initial values and can effectively accelerate convergence velocity of iteration.The innovation in this paper :(1) We introduce the classic nonlinear programming simplex algorithm and MDS algorithm, then make a comprehensive study and analysis. At the last of this part, we analysis the convergence of two algorithm.(2) In the basis of the classical nonlinear simplex algorithm, proposed a modified nonlinear simplex method .The modified algorithm used for addition to the worst point other than the remaining points of the weighted average as a reflection center, this is conducive to speed up the convergence rate. And the modified simplex algorithm using the "Parallel moving simplex method", this can guarantee simplex in the iterative process is not descend, not deformation.(3) Through the number of experiments, comparison the simplex method and the new algorithm, come to the conclusion that the new algorithm more effective.