A Parallel Levenberg-Marquardt Algorithm

This paper describes a parallel Levenberg-Marquardt algorithm that has been implemented as part of a larger system to support the kinetic modeling of polymer chemistry. The Levenberg-Marquardt algorithm finds a local minimum of a function by varying parameters of the function. The modeling system uses the algorithm to optimize the values of constants that describe the rate at which reactions proceed in a model of the chemical reaction. We present a detailed description of the Levenberg-Marquardt algorithm, and describe three levels of parallelization enabled by our algorithm. The performance and precision of our algorithm is compared to that of the IMSL package's implementation of the algorithm, using two models developed by the polymer chemistry research group at Purdue. Our experimental results show increased precision of the final result relative to the IMSL implementation. We also show good scaling with increased numbers of processors, compared to both a sequential version of our algorithm and against the IMSL implementation.