Perhaps you can show us what you’re tried, and the errors which occurred. You should presumably intimately understand the notation and conventions in the problem description, whereas forum readers should not be expected to have this understanding.
I would think you would get the values for the different \theta of what comes after max into a vector, which I’ll call joe_blow, and then the objective would be minimize(max(joe_blow)). The constraints look like a matter of correctly indexing, given whatever the notation and conventions are. So it appears to be a straightforward problem form a conic formulation perspective, with the subtlety of dealing correctly with the indexing.
And before you post, please carefully read