PCOMP: A Modeling Language for Nonlinear Programs with Automatic Differentiation

Abstract

PCOMP is a modeling language to facilitate the implementation of highly nonlinear equations arising in mathematical programming or in dynamical systems. Main applications are in engineering and natural sciences, where in addition to function values also first and second derivatives must be computed. In this paper, we briefly introduce the forward and reverse modes of automatic differentiation as implemented in PCOMP. Especially we show by means of a complex function that the relative effort for computing gradients by reverse accumulation is bounded. The structure of the PCOMP language and the usage of the software is outlined. To present a typical example, we show how PCOMP is attached to an interactive software system called EASY-FIT for estimating parameters in dynamical systems, where derivatives of the objective function, but also of initial values and right-hand sides of differential equations subject to different parameter sets must be computed.