I have the following parametric constrained quadratic optimization problem:
$\min_{x\in\mathbb{R}^n} \dfrac{1}{2}x^TK(\alpha)x+c(\alpha)^Tx$ subject to $Ax\preceq b$, $Cx=d$
where $\alpha\in[M_1,M_2]$ is the parameter with $0<M_1<M_2<\infty$ and $K(\alpha)\succeq 0$.
This is a convex problem and suppose for some $\alpha_0\in[M_1,M_2]$, the optimal solution to this problem is $x_{\alpha_0}$. Informally, my goal is to show that if I perturb $\alpha_0$ to some $\alpha_1\in[M_1,M_2]$ in this problem then $\|x_{\alpha_1}-x_{\alpha_0}\|\le \beta|\alpha_1-\alpha_0|$ where $\beta>0$ is a constant independent of $\alpha$.
I would really appreciate any hint or references which may be useful to get some sufficient conditions that guarantee this sort of a result. Thanks!