http://en.wikipedia.org/wiki/Least_squares

Lasso method

In some contexts a regularized version of the least squares solution may be preferable. The LASSO algorithm, for example, finds a least-squares solution with the constraint that | β | 1, the L1-norm of the parameter vector, is no greater than a given value. Equivalently, it may solve an unconstrained minimization of the least-squares penalty with α | β | 1 added, where α is a constant. (This is the Lagrangian form of the constrained problem.) This problem may be solved using quadratic programming or more general convex optimization methods. The L1-regularized formulation is useful in some contexts due to its tendency to prefer solutions with fewer nonzero parameter values, effectively reducing the number of variables upon which the given solution is dependent [3].