On constrained second derivatives
  The question of defining unique, generally applicable constrained second, and higher-order, derivatives is investigated. It is shown that second-order constrained derivatives obtained via two successive constrained differentiations provide a proper tool for the determination of the characters of stationary points under constraints. As an illustration, a finite-dimensional example is considered that has previously been used as an illustration for other stationary-point analysis methods. 
Tamas Gal
math-ph math.MP