  The first-order optimality conditions for a generic nonlinear optimization
problem are generated as part of the terminal transversality conditions of an
optimal control problem. It is shown that the Lagrangian of the optimization
problem is connected to the Hamiltonian of the optimal control problem via a
zero-Hamiltonian, infinite-order, singular arc. The necessary conditions for
the singular optimal control problem are used to produce an auxiliary
controllable dynamical system whose trajectories generate algorithm primitives
for the optimization problem. A three-step iterative map for a generic
algorithm is designed by a semi-discretization step. Neither the feedback
control law nor the differential equation governing the algorithm need be
derived explicitly. A search direction is produced by a proximal-aiming-type
method that dissipates a control Lyapunov function. New step size procedures
based on minimizing control Lyapunov functions along a search vector complete
the design of the accelerated algorithms.
