ldp: Least Distance Programming

Description

Solves the following inverse problem: $$\min(\sum {x_i}^2)$$ subject to $$Gx>=h$$

uses least distance programming subroutine ldp (FORTRAN) from Linpack

Usage

ldp(G, H, tol = sqrt(.Machine$double.eps), verbose = TRUE)

Arguments

numeric matrix containing the coefficients of the inequality constraints $Gx>=H$; if the columns of G have a names attribute, they will be used to label the output.

numeric vector containing the right-hand side of the inequality constraints.

tol

tolerance (for inequality constraints).

verbose

logical to print ldp error messages.

Value

a list containing:
Xvector containing the solution of the least distance problem.
residualNormscalar, the sum of absolute values of residuals of violated inequalities; should be zero or very small if the problem is feasible.
solutionNormscalar, the value of the quadratic function at the solution, i.e. the value of $\sum {w_i*x_i}^2$.
IsErrorlogical, TRUE if an error occurred.
typethe string "ldp", such that how the solution was obtained can be traced.

References

Lawson C.L.and Hanson R.J. 1974. Solving Least Squares Problems, Prentice-Hall

Lawson C.L.and Hanson R.J. 1995. Solving Least Squares Problems. SIAM classics in applied mathematics, Philadelphia. (reprint of book)

Examples

Run this code

# parsimonious (simplest) solution
G <- matrix(nrow = 2, ncol = 2, data = c(3, 2, 2, 4))
H <- c(3, 2)

ldp(G, H)