Um estudo sobre condições de otimalidade para problemas de otimização com restrições

Abstract

The objective of this work is to conduct a study on optimality conditions for constrained optimization problems. To this end, we have prepared a review of concepts with the main mathematical results that support the theory presented in the work. Additionally, we will introduce this theory through constrained optimization problems. We will focus on discussing and demonstrating the First Order Conditions, known as the Karush-Kuhn-Tucker Conditions (KKT Conditions), and the Second Order Conditions. For this purpose, we will briefly study cone theory, interpreting them as approximations of the feasible set. We emphasize that this work is intended for readers seeking an introductory reading on Constrained Optimization Theory.