  This paper introduces OptimizedDP, a high-performance software library that
solves time-dependent Hamilton-Jacobi partial differential equation (PDE),
computes backward reachable sets with application in robotics, and contains
value iterations algorithm implementation for continuous action-state space
Markov Decision Process (MDP) while leveraging user-friendliness of Python for
different problem specifications without sacrificing efficiency of the core
computation. These algorithms are all based on dynamic programming, and hence
can both be challenging to implement and have bad execution runtime due to the
large high-dimensional tabular arrays. Although there are existing toolboxes
for level set methods that are used to solve the HJ PDE, our toolbox makes
solving the PDE at higher dimensions possible as well as having an order of
magnitude improvement in execution times compared to other toolboxes while
keeping the interface easy to specify different dynamical systems description.
Our toolbox is available online at https://github.com/SFU-MARS/optimized_dp.
