ldp {limSolve} | R Documentation |
Solves the following inverse problem:
min(sum {x_i}^2)
subject to
Gx>=h
uses least distance programming subroutine ldp (FORTRAN) from Linpack
ldp(G, H, tol=sqrt(.Machine$double.eps), verbose=TRUE)
G |
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 |
H |
numeric vector containing the right-hand side of the inequality constraints |
tol |
tolerance (for inequality constraints) |
verbose |
logical to print ldp error messages |
a list containing:
X |
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 |
Karline Soetaert <k.soetaert@nioo.knaw.nl>
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)
ldei
, which includes equalities
# parsimonious (simplest) solution G <- matrix(nr=2,nc=2,data=c(3,2,2,4)) H <- c(3,2) ldp(G,H)