Unique polyhedral representations of continuous selections for convex multiparametric quadratic programs

A method which ensures uniqueness of the polyhedral partition of the parameter space for convex multiparametric quadratic programs (mp-QP) is presented. When the mp-QP has non-unique solutions, the norm of the solution vector is minimized and a unique affine optimizer function is identified for each region. It is proven, that under certain assumptions on the problem data, a globally continuous piecewise affine optimizer function is selected.