We consider a semi-preinvex programming as follows: $$ (\mbox{P})~~\left\{\begin{array}{l} \inf~f(x)\\ \mbox{ subject to}~x\in K\subseteq X,~g(x)\in -D,\end{array}\right . $$ where $K$ is a semi-connected subset; $f:K\to (Y,C)$ and $g:K\to (Z,D)$ are semi-preinvex maps; while $(Y,C)$ and $(Z,D)$ are ordered vector spaces with order cones $C$ and $D$, respectively. If $f$ and $g$ are arc-directionally differentiable semi-preinvex maps with respect to a continuous map: $\gamma :[0,1]\to K\subseteq X$ with $\gamma (0)=0$ and $\gamma '(0^+)=u$, then the necessary and sufficient conditions for optimality of (P) is established. It is also established that a solution of an unconstrained semi-preinvex optimization problem is related to a solution of a semi-prevariational inequality .