# Lagrangian Methods in Constrained Optimization

An expert is a person who has made all the mistakes that can be made in a very narrow field. - Niles Bohr

Network Engineer

An expert is a person who has made all the mistakes that can be made in a very narrow field. - Niles Bohr

The Median Isn’t the Message - Stephen Jay Gould

Two roads diverged in a wood, and I–I took the one less traveled by, And that has made all the difference.- Robert Frost

In a previous post, I discussed how Maximum Flow problems can be used for network optimization. We focused on a scenario where demands were already routed in the network, and our objective was to determine the maximum demand that could be handled between a given source and a destination metro. We solved this problem by calculating the residual bandwidth for the graph, creating fake demand nodes for each metro with high-capacity edges to avoid them being bottlenecks, and applying Dinic’s algorithm between the source and the destination metro. This is also called a Single Commodity Flow Problem.