Tree-sparse convex programs

Dynamic stochastic programs are prototypical for optimization problems with an inherent tree structure inducing characteristic sparsity patterns in the Karush–Kuhn–Tucker (KKT) systems of interior methods. We propose an integrated modeling and solution approach for such tree-sparse programs. Three closely related natural formulations are theoretically analyzed from a control-theoretic perspective and compared to each other. Associated KKT system solution algorithms with linear complexity are developed and comparisons to other interior approaches and related problem formulations are discussed.