Dynamic programming problem with dimension over 1000 I am working on a project which need to solve a dynamic programming problem with dimension over 1000. In past literature, there exist several methods like Smolyak algorithm and Sparse grid method that can solve dynamic programming problem with dimension no more than 100. My question is that does there exist such a brute force method that can solve problem with high dimension efficiently. Or I need to apply some approximation or reduce dimension.
Numerical Dynamic programming is always an approximation when any of the variables are continuous....

Depending on the structure of the problem, some people claim that you can apply linear programming techniques to approximate a solution. These guys MIT paper, claim that they have experiments that show that their linear reprogramming approximation is good enough.