If you relax the strictness criterion, then yes, you could pose your question as a constrained optimization problem:
\begin{align}
& \min_{\theta_{1}, \theta_{2}, \theta_{3}} f(\theta_{1}, \theta_{2}, \theta_{3}) \\
\textrm{s.t.} & \theta_{1} \geq \theta_{2} \geq \theta_{3}.
\end{align}
To approximate $\theta_{1} > \theta_{2} > \theta_{3}$, you could add a parameter $\varepsilon > 0$ such that:
\begin{align}
& \min_{\theta_{1}, \theta_{2}, \theta_{3}} f(\theta_{1}, \theta_{2}, \theta_{3}) \\
\textrm{s.t.} & \theta_{1} \geq \theta_{2} + \varepsilon \\
& \theta_{2} \geq \theta_{3} + \varepsilon
\end{align}
These variants of your constraints are linear, so provided that your function $f$ is well-behaved (smooth, easy to calculate, easy to compute derivatives, derivatives are well-conditioned, etc.), any constrained optimization solver should be able to solve your problem without issue.