In this project, we propose a new hybrid algorithm for parameter optimization and implement it using MPI. In
particular, we study a scalable parallel nonlinear parameter optimization algorithm with parameter pools for a
nonlinear dynamical system called the asset flow differential equations (AFDEs) in R4. We generate time series
pairs as proxy to market price and net asset value by using random walk simulation where the volatilities of the
time series are similar to that of real closed-end funds traded on New York Stock Exchange (NYSE). When we
apply the algorithm by using simulations for a set of time series, we observe that the computed optimal
parameter values, average number of quasi-Newton iterations, the average nonlinear least squares errors, and the
average maximum improvement factors can converge certain values within corresponding small ranges, after
oscillations. Moreover, we tested for 64, 128, 256 and 512 cores using the 512 initial parameter vectors. We
achieved speed-up for the time series to run up to 512 cores. The algorithm is applicable for parameter
optimization of the related nonlinear dynamical system of differential equations with thousands of parameters as
well
