A linear optimization problem can be transformed from a optimization problem to a feasibility problem by using the dual program:
A solution of $\min \{c^Tx : Ax \geq b\}$ is equivalent to finding a solution to $\{ Ax \geq b, y^TA=c^T, y\geq 0\}$
Is this also possible in case of a quadratic convex objective (H is positive semidefinite) with linear bounds?
How can i rewrite the minimization problem $\min \{x^TH x + d^Tx : l \leq x \leq u\}$ to an equivalent feasibility problem?
First note that convex quadratic program is not linear so you should not expect a linear counterpart duality sys for it , but using KKT condition you can characterize optimal solution by solving and quadratic inequalities .
KKT