Newton´s method for constrained norm minimization and its application to weighted graph problems

Due to increasing computer processing power, Newton´s method is receiving again increasing interest for solving optimization problems. In this paper, we provide a methodology for solving smooth norm optimization problems under some linear constraints using the Newton´s method. This problem arises in many machine learning and graph optimization applications. We consider as a case study optimal weight selection for average consensus protocols for which we show how Newton´s method significantly outperforms gradient methods both in terms of convergence speed and in term of robustness to the step size selection.