  We introduce an extension of Dual Dynamic Programming (DDP) to solve linear
dynamic programming equations. We call this extension IDDP-LP which applies to
situations where some or all primal and dual subproblems to be solved along the
iterations of the method are solved with a bounded error (inexactly). We
provide convergence theorems both in the case when errors are bounded and for
asymptotically vanishing errors. We extend the analysis to stochastic linear
dynamic programming equations, introducing Inexact Stochastic Dual Dynamic
Programming for linear programs (ISDDP-LP), an inexact variant of SDDP applied
to linear programs corresponding to the situation where some or all problems to
be solved in the forward and backward passes of SDDP are solved approximately.
We also provide convergence theorems for ISDDP-LP for bounded and
asymptotically vanishing errors. Finally, we present the results of numerical
experiments comparing SDDP and ISSDP-LP on a portfolio problem with direct
transation costs modelled as a multistage stochastic linear optimization
problem. On these experiments, ISDDP-LP allows us to obtain a good policy
faster than SDDP.
