ABSTRACT: We discuss how the well-known alternating direction method of multipliers (ADMM) can be used to solve distributed optimal control problems with constraints of linear parabolic equations. At each iteration, an unconstrained parabolic optimal control problem needs to be solved and this is the main computation Because of the high dimensionality after full discretization, it is more practical to just solve this subproblem inexactly (e.g., iteratively by the conjugate gradient method) up to medium accuracy, rather than exactly. Then, it becomes important to design an appropriate inexactness criterion for these inner iterations, that can guarantee both the overall convergence (with rigorous proof) and satisfactory numerical performance (avoiding unnecessarily high accuracy for subproblems). We discuss these issues, starting from a previous work on the ADMM for large-scale LASSO problems arising in statistical learning.
21-11-2019 4:15 PM Uhr bis 5:15 PM Uhr