Alternatives to conjugate direction optimization for sparse solutions to geophysical problems

Alternatives to conjugate direction optimization for sparse solutions to geophysical problems

Nader Moussa

Abstract:

Throughout much of this summer, we experimented with extensions to the conjugate direction method to find optimal solutions to sparse geophysical problems. However, this category of techniques is not unique in its ability to optimize L1-styled fitting goals. We also investigated a variety of other techniques, including a pure L1 solution via the weighted median; a steepest-descent algorithm using the signum-function as a gradient of the true L1 norm; and a totally different approach using the Simplex Algorithm, by mapping our objective function into a linear programming form. Categorically, the approaches that relied on the true L1 method failed due to what we believe is a theoretical shortcoming of the direct application of the pure L1 norm to geophysical optimization problems. The use of linear programming turned out to be quite successful. This could be an interesting option for future research in geophysical optimization.

Alternatives to conjugate direction optimization for sparse solutions to geophysical problems