A simplex method using line search

The paper presents an analysis of the simplex method. A simplex formed by Spendley is regular. But in a modification, Nelder and Mead have changed the regular simplexes into irregular ones. In this paper, an improvement using line search is made to the Nelder-Mead method, and the convergence of the improvement method is discussed. Finally, a comparison of the three algorithms is given in the convergence rate by two examples.