Stochastic Quadratic Dynamic Programming

We introduce an algorithm called SQDP (Stochastic Quadratic Dynamic Programming) to solve some multistage stochastic optimization problems having strongly convex recourse functions. The algorithm extends the classical Stochastic Dual Dynamic Programming (SDDP) method replacing affine cuts by quadratic cuts. We provide conditions ensuring strong convexity of the recourse functions and prove the convergence of SQDP. In the special case of a single stage deterministic problem, we call QCSC (Quadratic Cuts for Strongly Convex optimization) the method and prove its complexity. Numerical experiments illustrate the performance and correctness of SQDP, with SQDP being much quicker than SDDP for large values of the constants of strong convexity.