Large-Scale Nonlinear Programming: Decomposition Methods

The use of primal and dual methods are at the heart of finding solutions to large-scale nonlinear programming problems. Both methods are algorithms of a two-level type where the lower-level decision makers work independently to solve their individual subproblems generated by the decomposition of the original (overall) problem. At the same time, the upper-level decision maker solves his coordinating problem by using the results coming from the lower-level optimizations. These algorithms perform optimization calculations successively by an iterative exchange of information between the two levels.