Numeric.LinearProgramming.L1

Linear system solvers in the L_1 norm using linear programming.

Documentation

l1Solve

Arguments

:: Double

λ

-> Matrix Double

A

-> Vector Double

b

-> Vector Double

x

Solution in the L_1 norm, with L_1 regularization, of a linear system Ax=b.

argmin_x  λ||x||_1 + ||Ax-b||_1

l1SolveGT

Arguments

:: Double

λ

-> Matrix Double

A

-> Vector Double

b

-> Vector Double

x

Solution in the L_1 norm, with L_1 regularization, of a system of linear inequalities Ax>=b.

argmin_x  λ||x||_1 + ||step(b-Ax)||_1

l1SolveO :: Matrix Double -> Vector Double -> Vector Double

L_1 solution of overconstrained system Ax=b.

argmin_x ||Ax-b||_1

lInfSolveO :: Matrix Double -> Vector Double -> Vector Double

L_inf solution of overconstrained system Ax=b.

argmin_x ||Ax-b||_inf

l1SolveU :: Matrix Double -> Vector Double -> Vector Double

L1 solution of underconstrained linear system Ax=b.

argmin_x ||x||_1 such that Ax=b