  This paper proposes several novel optimization algorithms for minimizing a
nonlinear objective function. The algorithms are enlightened by the optimal
state trajectory of an optimal control problem closely related to the minimized
objective function. They are superlinear convergent when appropriate parameters
are selected as required. Unlike Newton's method, all of them can be also
applied in the case of a singular Hessian matrix. More importantly, by
reduction, some of them avoid calculating the inverse of the Hessian matrix or
an identical dimension matrix and some of them need only the diagonal elements
of the Hessian matrix. In these cases, these algorithms still outperform the
gradient descent method. The merits of the proposed optimization algorithm are
illustrated by numerical experiments.
