  In [13], an Inexact variant of Stochastic Dual Dynamic Programming (SDDP)
called ISDDP was introduced which uses approximate (instead of exact with SDDP)
primal dual solutions of the problems solved in the forward and backward passes
of the method. That variant of SDDP was studied in [13] for linear and for
differentiable nonlinear Multistage Stochastic Programs (MSPs). In this paper,
we extend ISDDP to nondifferentiable MSPs. We first provide formulas for
inexact cuts for value functions of convex nondifferentiable optimization
problems. We then combine these cuts with SDDP to describe ISDDP for
nondifferentiable MSPs and analyze the convergence of the method. More
precisely, for a problem with T stages, we show that for errors bounded from
above by epsilon, the limit superior and limit inferior of sequences of upper
and lower bounds on the optimal value of the problem are at most at distance
3*epsilon*T to the optimal value and that for asymptotically vanishing errors
ISDDP converges to an optimal policy.
  [13] V. Guigues, Inexact cuts in Stochastic Dual Dynamic Programming, Siam
Journal on Optimization, 30(1), 407-438, 2020.
