Conjunto simpléticos e otimização: métodos simplex e Nelder-Mead

Abstract

It’s common to use numerical techniques for solving problems to minimize, or maximize mathematical functions. Basead on this, the present work makes an explantion of two simpletical methods of derivate free optimization. Initialy a brief study was made on the concept in convex analysis to define a symplectic set. Then, an introduction was made to the problems of linear programming and their caracteristics. To solver these problems a study of the Simplex Method was approached, which consists of minimization an objective function using only basics matrix operations. With the algorithm of the Simplex Method done, the next step of this work was to study nonlinear programming problems to introduce the algorithm of the Nelder-Mead Method. About this algorithm, we present a theoretical study of the method, proving some properties and bringing their advantages and disadvantages to use the Nelder-Mead Method with a small variation of the classic method in the literature.