Consider the quadratic program:
$$\psi \in \underset{\xi \in (\mathcal{X} - a)}{\operatorname{arg min}} - \xi'S + \frac{1}{2}\xi' W \xi \, , $$ where $\mathcal{X}$ is a convex subset of $\mathbb{R}^d$, $a$ is $d \times 1$ vector, $S$ is a $d \times 1$ vector, and $W$ is a $d \times d$ PSD symmetric matrix. Consider the alternative program:
$$\psi^* \in \operatorname{arg min}_{\xi \in (\mathcal{X} - b)} - \xi'S + \frac{1}{2}\xi' W \xi \, , $$ where $b$ is a $d \times 1$ vector. How to find a nontrivial upper bound for $||\psi - \psi^*||_2$ as a function of $||a - b||_2$ (and possibly other terms)?