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:

vector containing the solution of the least distance problem.

residualNorm

scalar, the sum of absolute values of residuals of violated inequalities; should be zero or very small if the problem is feasible.

solutionNorm

scalar, the value of the quadratic function at the solution, i.e. the value of $\sum {w_i*x_i}^2$.

IsError

logical, TRUE if an error occurred.

type

the string "ldp", such that how the solution was obtained can be traced.

numiter

the number of iterations.

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

# NOT RUN {
# parsimonious (simplest) solution
G <- matrix(nrow = 2, ncol = 2, data = c(3, 2, 2, 4))
H <- c(3, 2)

ldp(G, H)
# }