This is an example programming model of ODMO program.
$$
\begin{align}
\underset{\boldsymbol{x} = [x_1, x_2]^T}{\min} & \quad \boldsymbol{c}^T \boldsymbol{x} \\
\text{s.t.} & \quad F(\boldsymbol{x}) \triangleq \boldsymbol{F}_0 + x_1 \boldsymbol{F}_1 + x_2 \boldsymbol{F}_2 \geq 0 \\
& \quad \boldsymbol{F}_0, \boldsymbol{F}_1, \boldsymbol{F}_2 \in \mathbb{R}^{2 \times 2}, \boldsymbol{c} \in \mathbb{R}^2
\end{align}
$$
[Set] appropriate values below to describe your problem.