Search

This paper deals with the numerical solution of optimal control problems for ODEs. The methods considered here rely on some standard optimization code to solve a discretized version of the control problem under consideration. We aim to make available to the optimization software not only the discrete objective functional, but also its gradient. The objective gradient can be computed either from forward (sensitivity) information or backward (adjoint) information. The purpose of this paper is to discuss various ways of adjoint computation. It will be shown both theoretically and numerically that methods based on the continuous adjoint equation require a careful choice of both the integrator and gradient assembly formulas in order to obtain a gradient consistent with the discretized control problem. Particular attention is given to automatic differentiation techniques which generate automatically a suitable integrator. [ABSTRACT FROM AUTHOR]

Object-oriented programming is a relatively new tool in the development of optimization software. The code extensibility and the rapid algorithm prototyping capability enabled by this programming paradigm promise to enhance the reliability, utility, and ease of use of optimization software. While the use of object-oriented programming is growing, there are still few examples of general purpose codes written in this manner, and a common approach is far from obvious. This paper describes OPT++, a C++ class library for nonlinear optimization. The design is predicated on the concept of distinguishing between an algorithm-independent class hierarchy for nonlinear optimization problems and a class hierarchy for nonlinear optimization methods that is based on common algorithmic traits. The interface is designed for ease of use while being general enough so that new optimization algorithms can be added easily to the existing framework. A number of nonlinear optimization algorithms have been implemented in OPT++ and are accessible through this interface. Furthermore, example applications demonstrate the simplicity of the interface as well as the advantages of a common interface in comparing multiple algorithms. [ABSTRACT FROM AUTHOR]