Generalized-norm conjugate direction solver

Generalized-norm conjugate direction solver

Mohammad Maysami and Nader Moussa

Abstract:

In optimization problems, the $L_1$ norm outperforms the $L_2$ norm in presence of noise and when a blocky or sparse solution is appropriate. These applications call for a solver that can redefine the optimum criteria for a particular problem. We have implemented a generalized norm solver that is useful for a wide range of problems. Our solver modularizes the norm function so that it can easily be interchanged to experiment with different schemes on any particular geophysical problem. We implement $L_1$, $L_2$, and two additional norms: Huber and Hybrid $L_1/L_2$. These are useful for problems that seek the benefits of both the $L_1$ and $L_2$ norms.