  Inverse problem for the identification of the parameters for large-scale
systems of nonlinear ordinary differential equations (ODEs) arising in systems
biology is analyzed. In a recent paper in \textit{Mathematical Biosciences,
305(2018), 133-145}, the authors implemented the numerical method suggested by
one of the authors in \textit{J. Optim. Theory Appl., 85, 3(1995), 509-526} for
identification of parameters in moderate scale models of systems biology. This
method combines Pontryagin optimization or Bellman's quasilinearization with
sensitivity analysis and Tikhonov regularization. We suggest modification of
the method by embedding a method of staggered corrector for sensitivity
analysis and by enhancing multi-objective optimization which enables
application of the method to large-scale models with practically
non-identifiable parameters based on multiple data sets, possibly with partial
and noisy measurements. We apply the modified method to a benchmark model of a
three-step pathway modeled by 8 nonlinear ODEs with 36 unknown parameters and
two control input parameters. The numerical results demonstrate geometric
convergence with a minimum of five data sets and with minimum measurements per
data set. Software package \textit{qlopt} is developed and posted in GitHub.
MATLAB package AMIGO2 is used to demonstrate advantage of \textit{qlopt} over
most popular methods/software such as \textit{lsqnonlin}, \textit{fmincon} and
\textit{nl2sol}.
