Variational calculus for descriptor problems

The first-order, necessary condition for optimality is derived from a variational argument that involves an ad hoc modification of the Bliss method, resulting in a Hamiltonian characterization in terms of Edx,dt, rather than dx/dt, the former being smoother than the latter. This approach sidesteps the regularity conditions of the Lagrange multiplier theory. Under some mild assumptions, the necessary condition for optimality is also sufficient and the optimal control exists. The numerically relevant result is a generalized eigenvector, inverse-free characterization of optimality