We propose some automatic techniques for unconstrained optimization with the objective function given by some computer program. We show that the Newton step can be calculated in O(m2) operations where m is the number of stages in the function evaluation program. We also show that methods developed in Coleman and Liao  and Liao  for unconstrained discrete-time optimal control problems can be modified to handle general cases.
theory center; discrete-time optimal control; stagewise Newton's method; trust region method; automatic differentiation
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