$$\min \; x^T Q x \\ s.t. Ax\le b $$
With $Q$ being PSD, is the optimal solution unique?
To add more detail, the objective function I am interested in is $ \sum x_i ^2 $. For the linear case it is well known that the optimal solution may not be unique. For an unconstrained quadratic problem it is intuitive, based on convexity, that the optimum is unique. For an equality constrained problem, one can express the optimal solution in terms of the KKT system of equations, which has a unique solution. How to go about showing that for an inequality constrained problem the optimal solution is (or it is not) unique?