Uma introdução às funções invexas diferenciáveis com aplicações em otimização

The notion of invex functions was introduced by Hanson in 1981as a generalization of convex functions. In fact, let $f: \Re^n\rightarrow \Re$ be a differentiable function. The function $f$is called invex if there exists a map $\eta : \Re^n \times \Re^n\rightarrow \Re^n$ such that, for all $x,u \in \Re^n$,\[f(x) - f(u) \geq f'(u) \cdot \eta(x,u).\]The convex case corresponds to $\eta(x,u)=x - u$. It isremarkable that many results in optimization involving convexfunctions actually hold for invex functions. In this article wecompile some of these results.