Lagrangian approach for large-scale least absolute value estimation

Abstract

With the proliferation of personal computers and the increased interest in robust estimation, a capability of efficiently solving large-scale least absolute value (LAV) problems on a microcomputer would be useful. Least absolute value estimation has gained wide acceptance as a robust alternative to least squares. This paper presents an algorithm for least absolute value estimation which utilizes a Lagrangian decomposition, so that only a small percentage of the linear programming constraints need to be considered during an iteration. One advantage of this method is that it provides the capability of solving large-scale LAV problems on a system where memory requirements are a consideration.