We consider the parametric programming problem (Qp) of minimizing the quadratic function f(x, p) := xT Ax + bT x subject to the constraint Cx ≤ d, where x ∈ ℝn, A ∈ ℝn×n, b ∈ ℝn, C ∈ ℝm×n, d ∈ ℝm, and p := (A, b, C, d) is the parameter. Here, the matrix A is not assumed to be positive semidefinite. The set of the global minimizers and the set of the local minimizers to (Qp) are denoted by M(p) and Mloc(p), respectively. It is proved that if the point-to-set mapping Mloc (·) is lower semicontinuous at p then Mloc(p) is a nonempty set which consists of at most 𝒜m,n points, where 𝒜m,n = (min{[m/2],n} m) is the maximal cardinality of the antichains of distinct subsets of {1, 2, ..., m} which have at most n elements. It is proved also that the lower semicontinuity of M(·) at p implies that M(p) is a singleton. Under some regularity assumption, these necessary conditions become the sufficient ones.
