Differential properties of the minimum function for diagonalizable quadratic problems

Abstract

For the problem of minimizing a quadratic functional subject to quadratic equality constraints, the topological and differential properties of the minimum function are examined. It is assumed that all the quadratic forms appearing in the statement of the problem are determined by simultaneously diagonalizable matrices. Under this assumption, sufficient conditions for the minimum function to be Lipschitzian are derived, and a description of the set on which this function may not be differentiable, is given.