Let's say we have the convex quadratic programming problem of minimizing function: $f=\frac{1}{2}X^TAX+b^TX$ with constraints: $C^TX\geq0$
If $b$ is dependent on a variable $y$, is there any way to calculate the derivative $\frac{dX}{dy}$? From some first calculations, these derivatives seem to be the solution of the linear programming problem: $\Delta f=(X^TA+b)\Delta X+\Delta b^TX$
However, I don't know if $\Delta b$ can be considered a constant term, so it can be disregarded for minimizing the LP objective function. Furthermore, the constraints of the LP problem must be the active constraints of the QP, but with the derivatives $\Delta X$ instead of $X$.
Can you comment on this approach? Thank you!
EDIT: For anyone interested, see paper: On sensitivity analysis in convex quadratic programming problems, J.C.G.Boot (1963)