A Dual Dynamic Programming for Multidimensional Elliptic Optimal Control Problems
E. Galewska, Andrzej Nowakowski · Numerical Functional Analysis and Optimization · 2006
This paper deals with the optimal control problems with multiple integrals and an elliptic partial differential equation. The sufficient conditions for optimality in these problems are proved through a dual dynamic programming. The concept of an optimal dual feedback is introduced, and the theorem guaranteeing its existence is established. For the purposes of numerical methods, the ε-version of the verification theorem provided appears to be very useful.