Multi-intersected/recursive textured algorithms for large-scale convex optimization problems

In this paper, we extend our textured algorithm to multi-intersected textured models. We also describe the recursive textured decomposition process as a tree, in which we can obtain the overall solution by consolidating the end subsystem solutions. The proposed algorithms, their properties, and the theorems for exact convergence are then addressed. The worst-case time complexity of the algorithm with complete tree structure, in which parents in the same recursion level have the same number of children, is analyzed. Examples are given to demonstrate the use of the algorithms and the trade-off among the number of recursion levels, the number of sequential computing steps, and problem size reduction.