  We address the question of whether the primal-dual approach for the design and analysis of online algorithms can be applied to nonmonotone problems. We provide a positive answer by presenting a primal-dual analysis to the online algorithm of Awerbuch et al.[AAPW01] for routing virtual circuits with unknown durations. 
A Nonmonotone Analysis with the Primal-Dual Approach: online routing of   virtual circuits with unknown durations