Newton's method for constrained norm minimization and its application to weighted graph problems
Résumé
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.