20 January 2000

14:00

Prof Bruce Christianson

Abstract

In 1983 Pantoja described a stagewise construction of the exact Newton
direction for a discrete time optimal control problem. His algorithm
requires the solution of linear equations with coefficients given by
recurrences involving second derivatives, for which accurate values are
therefore required.
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Automatic differentiation is a set of techniques for obtaining derivatives
of functions which are calculated by a program, including loops and
subroutine calls, by transforming the text of the program.
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In this talk we show how automatic differentiation can be used to
evaluate exactly the quantities required by Pantoja's algorithm,
thus avoiding the labour of forming and differentiating adjoint
equations by hand.
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The cost of calculating the newton direction amounts to the cost of
solving one set of linear equations, of the order of the number of
control variables, for each time step. The working storage cost can be made
smaller than that required to hold the solution.