I've been working with the following optimization problem:

$$ \max \int \left(\frac{1}{2}\left\| x \right\|^2 + \tilde{u}(x)\right) \,ds(x) + \int \left(\frac{1}{2}\left\| y \right\|^2 + \tilde{v}(y) \right) \,dt(y) $$ s.t. $\forall x,y,\quad \tilde{u}(x)+\tilde{v}(y) \leq -\langle x,y\rangle.$

Currently, I'm trying to understand stability/sensitivity of optimal solutions to small changes in $s$ and $t$.

I haven't found anything similar in the literature that covers this, so I'm wondering where I can begin. If you know a good reference, feel free to send that my direction.

Thanks!