Um compêndio do cálculo diferencial em espaços normados com aplicações em otimização contínua

Abstract

In this work, we present a compendium on differential calculus in normed spaces and address classic theorems and their extensions to infinite-dimensional spaces. Furthermore, we also explore applications in continuous optimization, including first and second-order optimality conditions and their generalizations. Our objective is to provide accessible and rigorous material that also highlights the importance of differential calculus in the formulation and resolution of optimization problems.