We present an ongoing effort to build a framework and a library in Isabelle/HOL for formalising primal-dual arguments for the analysis of algorithms. We discuss a number of example formalisations from the theory of matching algorithms, covering classical algorithms like the Hungarian Method, widely considered the first primal-dual algorithm, and modern algorithms like the AdWords algorithm, which models the assignment of search queries to advertisers in the context of search engines.

A formal mathematical library of graph-theoretic results. Focus is on algorithmic results.