Is there any cumulative constraint propagation technique for dynamic programming?

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I have a problem with the following two properties:

  • Overlapping Subproblems
  • Optimal Substructure (an optimal solution can be constructed efficiently from optimal solutions of its subproblems)

However, I have a cumulative nonlinear (but convex) constraint. I have the following questions and asking for your guidance:

  • Are model predictive control and dynamic programming optimization algorithms applicable to problems which have cumulative constraints?
  • Is there any cumulative constraint propagation techniques for dynamic programming?