Condições de otimalidade em programação não linear

Abstract

Optimization is an area of Mathematics whose objective is to study problems that consist of maximizing or minimizing functions. An optimization problem can be restricted or unrestricted, linear or nonlinear, convex or nonconvex, differentiable or nondifferentiable. This work aims to study the optimality conditions in nonlinear programming, for restricted and unrestricted problems. For optimization problems without restriction, a necessary condition for a point to be a candidate to minimize the objective function is that it be a critical point. In addition, it is possible to classify the nature of this point with the analysis of the Hessian matrix of f. For problems with restrictions, of equality or inequality, the optimality conditions are presented through the theory of Lagrange Multipliers.